Postpublished at 13:00 BST 27 May 2016
Murray 6-1 3-1 *Karlovic
Andy Murray cruise-controls through another service game, ticking along to 15.
The Briton has lost just four of the 26 points in which he has landed with his first serve.
Murray wins 6-1 6-4 7-6 (7-3)
Faces John Isner or Teymuraz Gabashvili next
Click audio icon to listen to commentary
* denotes next to serve
Mike Henson
Murray 6-1 3-1 *Karlovic
Andy Murray cruise-controls through another service game, ticking along to 15.
The Briton has lost just four of the 26 points in which he has landed with his first serve.
Sporting mis-matches (in size!)
Irfan is seven foot one, Taylor is five foot six.
An extra long portrait shot is necessary to squeeze them both in.
#bbctennis
Matt Taggart: Has Murray been drawn against the 2 oldest men (Stepanek and Karlovic - 37) at the French Open?
Yep, I believe so Matt.
*Murray 6-1 2-1 Karlovic
Andy Murray attempted a naughty little repeat of the lighthouse lob that he pulled off in the first set.
Just a little overcooked with Ivo Karlovic looking back at the baseline like a lost puppy.
The Croat is settling into his shooting boots, blasting his way to a hold to love.
But like in the first set the damage might already have been done with Murray a break up.
Murray 6-1 2-0 Karlovic*
Andy Murray was made to work harder in that service game, finally getting the job done of his second serve at 40-30 up.
But you feel that the Scot has a couple more gears the crunch through if the scoreboard needs perking up.
As it is, the numbers are looking lovely for the Briton.
*Murray 6-1 1-0 Karlovic
Ivo Karlovic had to come through his own five-set epic in the last round, winning 12-10 in the decider against Australia's Jordan Thompson.
It looks like the Croat is feeling every day of his 37 years as well.
He plants a gimme of a forehand volley wide to hand the game to Murray after a double fault had brought up 30-40.
Alix Ramsay
Journalist, The Scotsman, on BBC Radio 5 live sports extra
"Murray has always said that players mature later these days because of the fitness in the game. A spindly teenager just doesn't have the power to compete with somebody like Andy Murray and the older players, like Ivo Karlovic, are lasting longer."
Sporting mis-matches (in size!)
You might need to drop the high fives a bit lower, Peter...
Simon Duke on Facebook: The one I remember was when England were bringing on 2 subs and they were stood next to each other on the touchline - Shaun Wright-Phillips and Peter Crouch!
#bbctennis
Alice Stainer: Murray is surely one of the only players with both the gall & the skill to lob a 6ft 11 giant! The man's got style.
Murray 6-1 *Karlovic
Twenty-four minutes and Andy Murray has the first set wrapped up.
If he is trying to claw back some minutes after working overtime in the first two rounds, it is working.
*Murray 5-1 Karlovic
Normal, for Ivo, service begins.
Massive serving, two aces and a game whistling past Andy Murray to love at the speed of the Tokyo-to-Kyoto express.
Murray 5-1 *Karlovic
Andy Murray closes the match with a ramrod ace straight down the T.
Ivo Karlovic showed that when he gets a read on the Murray second serve, he is dangerous.
One string-stretching 102mph return practically came with cartoon "Pow!" subtitles.
As long as Murray keeps up a good hit-rate with his first serve though, that will keep the Croat at bay.
*Murray 4-0 Karlovic
Andy Murray thwacks the red dust off the soles of the hefty supportive trainers that he wears and serves the matches first ace to move 40-30 to the good.
Ivo Karlovic has shown a little more on return so far in this game, clouting one exocet forehand past Murray.
Maybe that gets in the British number one's head a little. His first double-fault takes the game to deuce.
*Murray 4-0 Karlovic
When Andy Murray feels comfortable enough on court to congratulate his opponent on a deft drop-shot this early on, you know he is in the groove.
Ivo Karlovic shows a nice touch to pull Murray back from 0-30 to 15-30 and earns an appreciative "oh yes" from the Scot.
But Karlovic double-faults for the third time in the match to offer up another break point and 30-40.
Murray's deep return, right up on the baseline, gets all up into Karlovic's ribs.
The Croat swats at it like a pesky wasp at a picnic, but that is net-bound.
Murray a double break to the good.
BBC Sport on Facebook
BBC Sport's Facebook users have made some suggestions about sporting mis-matches (in size!):
Lewis Skinner: Rey Mysterio vs The Great Khali.
We can't put our finger on a picture of these WWE peeps together, so here's one of The Great Khali with some other wrestlers. He is huge (on the left).
Murray 3-0 *Karlovic
Is that the first set on toast then?
Ivo Karlovic does not lose his serve very often, but he doesn't break his opponents all that much either.
The Croat is made to look lumbering compared to Murray's staccato footwork and is stretched all out of shape by the British number one's precise piercing groundstrokes.
*Murray 2-0 Karlovic
A squeal from the sidelines. Ivo Karlovic turns that laser stare sideways at the line judge who has foot-faulted him on second serve.
A brave man/woman.
Break point Murray. And he takes it with a brilliant lob, fizzing with topspin!
It needed every last inch of court to get it over Karlovic and back down inside the baseline.
Murray 1-0 Karlovic*
Andy Murray doesn't need any sighters.
He is immediately snapping away at the Ivo Karlovic serve, racking up 0-30.
He chases down a patter-cake volley into midcourt as Karlovic comes clanking into the net and slaps away a forehand down the line for 0-40 and three break points.
Maybe it is Karlovic who needed the sighters.
The Croat serves into the body, out wide and then into the body once more to take the game to deuce.
Murray 1-0 Karlovic*
Ivo Karlovic won the toss, but opted to receive rather than tee off that bazooka serve.
A bit of gamesmanship? A chance to loosen off the limbs?
Who knows?
It doesn't throw Murray though who breezes through his opening service game to 15.
Murray v Karlovic
Andy Murray has spent seven hours and 14 minutes on court so far at Roland Garros.
Imagine taking a flight from London to New York, but instead of trying to watch a blockbuster on a small murky screen, sprinting and skidding up the aisle for the duration of the flight.
That is the sort of toll that his opening two matches will have taken.
He has dropped 39 games already. Martina Navratilova lost just 19 in the whole of her run to the 1983 US Open title.