The third-seeded Murray was broken in the opening game of the first set, but he immediately broke back to make it 1-1.
"After that, I was very happy with the way I played," Murray said of the early break. "I wasn't expecting to play that well in the first match."
The Scot was rarely threatened after that, although Chela did manage another break. Murray finished the match with eight breaks of serve, 55 winners and 10 aces.
Murray looked rusty early, but he soon began to hit hard groundstrokes and move Chela around the court. While Murray only had four fewer unforced errors -- 19 to Chela's 23 -- the Briton had 41 more winners.
"Chela is a tough player," Murray said. "I understood what I had to do today. I didn't take Chela lightly at all."
The 26th-seeded Karlovic, who has lost in the first round in 14 of his 24 Grand Slam appearances, broke the previous record of 51, which he shared with Joachim Johansson. The old mark for aces in a French Open match was 37, held by Andy Roddick.
"To play him on any surface, he's so dangerous," Hewitt said of Karlovic. "[He served] a lot of unreturnables with that as well."
At Wimbledon in 2003, Hewitt lost to Karlovic to become the first man in the Open era to lose in the first round as defending champion at the All England Club.
"The angle he gets, you can't touch a lot of his serves," Hewitt said. "It's physically impossible."
This time, as the 26th-seeded Karlovic tired in heat that topped 80 degrees, Hewitt grew more and more comfortable, and the two-time major champion's bothersome hip looked fine while he climbed all the way back.
How could a player who compiles 55 aces possibly lose?
"Don't know," was Hewitt's simple reply.
Karlovic was similarly befuddled, saying, "It is difficult to explain."
"Every round is a tough one," said Safin, who is planning to retire at the end of the season. "I'm trying but I'm really suffering on the court right now. But I'll try to play better next match and I hope that I will get through."
Seventh-seeded Gilles Simon, No. 8 Fernando Verdasco, No. 13 Marin Cilic of Croatia, No. 14 David Ferrer of Spain, No. 18 Radek Stepanek of the Czech Republic and No. 31 Nicolas Almagro of Spain also advanced.
Information from The Associated Press was used in this report.