After gruelling five-setters in his first two rounds, the second seed gave a masterclass in nullifying the game's biggest serve, breaking twice in succession at the start of the match to set up a 6-1 6-4 7-6(3) victory.
Murray will next face either American 15th seed John Isner, another big server, or Russian Teymuraz Gabashvili.
"Any match you play, the quicker you get it done, the better, especially in these events when the best of five it can go long," Murray told reporters.
"So it was nice to win quickly today. I spoke about that the other day, if it was possible to get this one done quickly, it gives me a chance to kind of recover from the first few days, which is good."
Karlovic had won 95 percent of his service games in the last year, more than any other player, but that counted for little on Court Suzanne Lenglen.
"It's a match-up that I like. I have had good success against him in the past and I have always enjoyed playing against serve and volleyers, normally," Murray said.
Karlovic was 4-0 behind in quick time as Murray toyed with the 6ft 11in player who was the oldest man to reach the third round of a grand slam for 25 years.
He even managed to send a couple of lobs looping over the head of Karlovic who looked jaded after coming through a five-setter in round two.
Having taken the second set with a single break, Murray's progress slowed in the third as Karlovic found his range to force a tiebreak.
But Murray stayed focussed and wrapped up a no-nonsense win on his first match point when the 27th seed sprayed a forehand well wide.
(Editing by Ed Osmond)
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