Murray, a three-time semi-finalist, had needed two five-set matches and three days of play to get to the last 32.
But on Friday the 29-year-old needed just a shade under two hours to beat 6ft 11in (2.11m) Karlovic 6-1, 6-4, 7-6 (7/3).
It was his seventh win in seven matches against the 37-year-old as Murray goes on to face either John Isner of the United States or Teymuraz Gabashvili of Russia.
"I was glad to win that tiebreak at the end."
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Canada's eighth seed Milos Raonic overcame a left hip injury to defeat Slovakian lucky loser Andrej Martin, the world number 133, and reach the last 16 for a second time.
Raonic won 7-6 (7/4), 6-2, 6-3 but only after requiring a medical timeout at the start of the third set to treat a hip injury.
The Canadian, plagued by a similar injury after reaching the Australian Open semi-finals in January, then needed to take a pain-killer before racing away to victory.
"The trainer was able to assure me that from what he could tell there was nothing serious."
Raonic, a quarter-finalist in 2014, next faces 55th-ranked Albert Ramos-Vinolas after the Spaniard stunned American 23rd seed Jack Sock 6-7 (2/7), 6-4, 6-4, 4-6, 6-4.
Ramos-Vinolas, 28, had not won a match at Roland Garros since 2011 before this year.
Spanish fourth seed and last year's Wimbledon runner-up Garbine Muguruza won the last nine games to knock out Belgium's Yanina Wickmayer 6-3, 6-0.
Romanian sixth seed Simona Halep, the runner-up to Maria Sharapova in 2014, needed three sets to see off 18-year-old Japanese player Naomi Osaka 4-6, 6-2, 6-3.
Halep, 24, next faces 2010 finalist Sam Stosur who defeated 2015 runner-up Lucie Safarova of the Czech Republic 6-3, 6-7 (0/7), 7-5.
It was only Stosur's fourth win 15 meetings with Safarova who has been troubled for most of this season with a debilitating bacterial infection.