Well, after playing the game's biggest server today, he could run straight into the second-biggest in the fourth round.
Murray will play 15th seed John Isner, providing the American beats Teymuraz Gabashvili in his own third-round match.
Murray into the fourth round
Andy Murray was asked, to his obvious embarrassment, to show off his French by repeating his dinner order.
He goes for a bit of boeuf with frites and un salade vert.
Old school. Not a pasta twizzle in sight.
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Murray into the fourth round
Andy Murray: "It was very close especially in the third set. He fought right to the end. I started quickly and obviously it is great to get off court in a relatively quick match.
"It is not always up to you when you are playing a server as big as him. I have to be patient and wait for my opportunities."
Post update
Alix Ramsay
Journalist, The Scotsman, on BBC Radio 5 live sports extra
"Very good job, very well done. It was just the sort of performance that Murray wanted and needed. He's got through the first week, and has saved fuel for the fourth match."
Game, set and match Murray
Murray 6-1 6-4 7-6 (7-3) Karlovic
Andy Murray slam-dunks down a big serve and swivels to his box in celebration as Ivo Karlovic bends in vain.
Into the fourth round...
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Tie-break
*Murray 6-1 6-4 6-6 (6-3) Karlovic
Margins of millimetres.
Andy Murray's bold backhand just clips the baseline to preserve his mini-break. 5-2.
A whipped pass off the Karlovic serve and he has a double break and match points aplenty at 6-2.
Karlovic whacks down an ace to save the first. 6-3.
Tie-break
*Murray 6-1 6-4 6-6 (4-2) Karlovic
Ivo Karlovic gets on the tie-break scoreboard as he hammers away a smash.
3-1 Murray.
Make that 3-2 as Ivo Karlovic pins Murray like a butterfly to a board with a body serve.
Murray cracks down an ace and stays a mini-break ahead.
Post update
Murray 6-1 6-4 6-6 (3-0) *Karlovic
Andy Murray makes immediate inroads. The Scot chases back, spins on a lob and slaps across court to move a mini-break up in the very first point.
Murray ties down his first service point of the tie-break to make it 2-0.
Into a rally on the next and Ivo slices into the top of the net. 3-0.
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Post update
Murray 6-1 6-4 6-6 *Karlovic
A hold to love and we are into the shoot-out.
Murray's serve has been far sturdier so far in this set.
Post update
*Murray 6-1 6-4 5-6 Karlovic
Andy Murray gets a little look at a cross-court pass as Ivo Karlovic lumbers in.
That one is snared by the tape though. 30-0.
Murray gets his sights set as he slaps a winner across court to turn 40-00 to 40-15.
But it is too much of a gap to make up.
We are a Murray service hold from tie-break town.
Post update
Murray 6-1 6-4 5-5 *Karlovic
Andy Murray clouts down a big serve to seal the game.
Ivo Karlovic managed to nibble his fourth point off the Murray serve in this set, but that is all he is taking back to his stool.
EPACopyright: EPA
Post update
*Murray 6-1 6-4 4-5 Karlovic
A backhand volley framed into the net brings up 0-15 and makes the Karlovic camp queasy.
A missed first serve. Creaky, creaky. And then a rocket second serve down the T is good.
That is the way to calm the nerves. He doesn't lose another point in the game and the danger disappears in the rear view mirror.
Post update
Murray 6-1 6-4 4-4 *Karlovic
Andy Murray flicks away a forehand for 30-0 after running down a drop-shot with time to spare.
He fires down an ace to tie up the game to love.
If he keeps serving like this, maybe the risks in a tie-break are actually relatively small.
Post update
*Murray 6-1 6-4 3-4 Karlovic
If Andy Murray wants this match wrapped up in the most straightforward way possible, he had better get a shift on.
Ivo Karlovic continues to make the pace on the scoreboard as he dinks away a drop-volley to hold to 15.
A tie-break shoot-out could easily turn nasty for Murray.
Get Involved
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#bbctennis
Daniel Woods: Karlovic's backhand is very poor for a player ranked inside the top 30.
Post update
Murray 6-1 6-4 3-3 *Karlovic
Andy Murray has dropped just three points on serve so far in this set.
He wallops his way through a whistlestop hold to love. Time to have a probe to try and find the underbelly of this Karlovic serve.
Live Reporting
Mike Henson
All times stated are UK
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Latest PostBye for now
Naomi Broady in the women's doubles first round is the only other Briton in action today.
We will bring you news on how she got on and all the rest of the news, comment, seriousness and silliness from Paris on our website and app later.
Goodbye for now.
Stats
Murray v Karlovic
A quick look thorough the stats as they come fresh off the printer.
Andy Murray landed with 75% of his first serves, knowing that he could afford to take some pace off against Karlovic's relatively weak return.
He hit 34 winners, actually less than the 37 that Karlovic managed.
Karlovic was restricted to only 14 aces though by Murray's scurry. The Scot managed eight.
On court
Nick Kyrgios and Richard Gasquet - you might as well mix cola and sherbet.
It is an explosive cocktail they are serving up on Philippe Chatrier at the moment.
The panache of Gasquet is on top against the power of Kyrgios at the moment. The Frenchman leads 5-1 and is serving for the opener.
You can follow that one and all the rest of the day's scores on our appropriately named Live Scores page.
Isner up next?
What's up next for British tennis' kingpin then?
Well, after playing the game's biggest server today, he could run straight into the second-biggest in the fourth round.
Murray will play 15th seed John Isner, providing the American beats Teymuraz Gabashvili in his own third-round match.
Murray into the fourth round
Andy Murray was asked, to his obvious embarrassment, to show off his French by repeating his dinner order.
He goes for a bit of boeuf with frites and un salade vert.
Old school. Not a pasta twizzle in sight.
Murray into the fourth round
Andy Murray: "It was very close especially in the third set. He fought right to the end. I started quickly and obviously it is great to get off court in a relatively quick match.
"It is not always up to you when you are playing a server as big as him. I have to be patient and wait for my opportunities."
Post update
Alix Ramsay
Journalist, The Scotsman, on BBC Radio 5 live sports extra
"Very good job, very well done. It was just the sort of performance that Murray wanted and needed. He's got through the first week, and has saved fuel for the fourth match."
Game, set and match Murray
Murray 6-1 6-4 7-6 (7-3) Karlovic
Andy Murray slam-dunks down a big serve and swivels to his box in celebration as Ivo Karlovic bends in vain.
Into the fourth round...
Tie-break
*Murray 6-1 6-4 6-6 (6-3) Karlovic
Margins of millimetres.
Andy Murray's bold backhand just clips the baseline to preserve his mini-break. 5-2.
A whipped pass off the Karlovic serve and he has a double break and match points aplenty at 6-2.
Karlovic whacks down an ace to save the first. 6-3.
Tie-break
*Murray 6-1 6-4 6-6 (4-2) Karlovic
Ivo Karlovic gets on the tie-break scoreboard as he hammers away a smash.
3-1 Murray.
Make that 3-2 as Ivo Karlovic pins Murray like a butterfly to a board with a body serve.
Murray cracks down an ace and stays a mini-break ahead.
Post update
Murray 6-1 6-4 6-6 (3-0) *Karlovic
Andy Murray makes immediate inroads. The Scot chases back, spins on a lob and slaps across court to move a mini-break up in the very first point.
Murray ties down his first service point of the tie-break to make it 2-0.
Into a rally on the next and Ivo slices into the top of the net. 3-0.
Post update
Murray 6-1 6-4 6-6 *Karlovic
A hold to love and we are into the shoot-out.
Murray's serve has been far sturdier so far in this set.
Post update
*Murray 6-1 6-4 5-6 Karlovic
Andy Murray gets a little look at a cross-court pass as Ivo Karlovic lumbers in.
That one is snared by the tape though. 30-0.
Murray gets his sights set as he slaps a winner across court to turn 40-00 to 40-15.
But it is too much of a gap to make up.
We are a Murray service hold from tie-break town.
Post update
Murray 6-1 6-4 5-5 *Karlovic
Andy Murray clouts down a big serve to seal the game.
Ivo Karlovic managed to nibble his fourth point off the Murray serve in this set, but that is all he is taking back to his stool.
Post update
*Murray 6-1 6-4 4-5 Karlovic
A backhand volley framed into the net brings up 0-15 and makes the Karlovic camp queasy.
A missed first serve. Creaky, creaky. And then a rocket second serve down the T is good.
That is the way to calm the nerves. He doesn't lose another point in the game and the danger disappears in the rear view mirror.
Post update
Murray 6-1 6-4 4-4 *Karlovic
Andy Murray flicks away a forehand for 30-0 after running down a drop-shot with time to spare.
He fires down an ace to tie up the game to love.
If he keeps serving like this, maybe the risks in a tie-break are actually relatively small.
Post update
*Murray 6-1 6-4 3-4 Karlovic
If Andy Murray wants this match wrapped up in the most straightforward way possible, he had better get a shift on.
Ivo Karlovic continues to make the pace on the scoreboard as he dinks away a drop-volley to hold to 15.
A tie-break shoot-out could easily turn nasty for Murray.
Get Involved
Get Involved
#bbctennis
Daniel Woods: Karlovic's backhand is very poor for a player ranked inside the top 30.
Post update
Murray 6-1 6-4 3-3 *Karlovic
Andy Murray has dropped just three points on serve so far in this set.
He wallops his way through a whistlestop hold to love. Time to have a probe to try and find the underbelly of this Karlovic serve.