The American was broken early in the first set but won the second when Karlovic sent a forehand wide in the tiebreaker.
"I didn't have very good momentum at the start," said Blake, who recently started working with coach Kelly Jones. "The third set, I liked the way, when I did get my racket on it, how I was playing."
Despite serving 27 aces in the match, Karlovic allowed Blake to break serve in the third and ninth games of the third set.
Karlovic, who holds the record for serving the 78 aces in a match during a five-set loss to Radek Stepanek in the Davis Cup semifinals last month, double-faulted on the final point.
Spanish players Tommy Robredo and David Ferrer advanced to the second round with straight-set wins.
The 14th-seeded Robredo, who won 29 of 31 points on his first serve and never faced a break point, easily beat French qualifier Michael Llodra 6-1, 6-4, while Ferrer beat Richard Gasquet 6-4, 6-3.
"Obviously it's a lot of matches to arrive at the (later) rounds, but for the moment, today, I played the first one and I won, and I'm very happy," Robredo said.
Tenth-seeded Fernando Gonzalez of Chile moved into the second round after Mischa Zverev of Germany retired with an injured right wrist with the score 7-5, 6-7 (0), 2-2.
Zverev played three games after falling during the first game but was unable to hit a backhand after the injury.
"I don't feel my best now, but I'm glad I'm keeping winning," Gonzalez said. "I'm trying my best, but sometimes you don't find the way that you really want to be."
Former Grand Slam champion Marat Safin, coming off of a quarterfinal showing at Beijing last week, beat Chinese wild-card entry Gong Maoxin 6-4, 6-4.