The world No. 2 and second-seeded Scot was two points from defeat as he rallied from a two-set deficit against Radek Stepanek in the first round and overcame French wildcard Mathias Bourgue to prevail in five sets on Wednesday.
Murray, 29, has never lost to 6-foot-11 Karlovic of Croatia in seven matches but this marked their first meeting on clay. Friday's match lasted just one hour and 56 minutes, compared to Murray's previous two matches in Paris with an average length of 3 1/2 hours.
"Especially at the end, it was very close in the third set," Murray said in his on-court interview. "I got off to a quick start (in the match) and against someone like Ivo, that's important. He fought right to the end and made it very tough. I'm obviously glad to win the tie-break and get off after a fairly quick match.
"The return has normally been the strongest part of my game, but even still, against him, it's not always up to you. When he serves well, there's not much you can do. I just try to stay patient and take care of my own service games."
Murray will play the winner of American John Isner, seeded No. 15, and Teymuraz Gabashvili of Russia for a place in the quarterfinals.
Eighth seed Milos Raonic of Canada continued his flawless progress at Roland Garros as he advanced to the fourth round with a 7-6 (4), 6-2, 6-3 victory over Andrej Martin of Slovak Republic. Raonic has yet to drop a set in Paris to reach the fourth round for the second time.
Next up for Raonic will be Spaniard Albert Ramos-Vinolas, who beat the 23rd seed, American Jack Sock, 6-7 (2), 6-4, 6-4, 4-6, 6-4. Sock, who reached the fourth round in Paris last year, led by a set and 4-1 but Ramos-Vinolas fought back to claim the win and securing his place in the fourth round of a major for the first time.
On the women's side, American Shelby Rogers, ranked 108th in the world, reached the fourth round, stunning two-time Wimbledon champion Petra Kvitova of the Czech Republic.
The 23-year-old Rogers from South Carolina reached the round of 16 at a Grand Slam tournament for the first time by upsetting the 10th-seeded Kvitova.
No.4 seed Garbine Muguruza of Spain brushing aside Yanina Wickmayer of Belguim 6-3, 6-0.
Sixth-seeded Simona Halep of Romania, the the 2014 runner-up, dropped the first set before rebounding to beat 18-year-old Naomi Osaka of Japan 4-6, 6-2, 6-3.