The seventh-seeded Croat saved a match point with an ace when trailing 6-5 in the third-set tiebreaker, then clinched the match with another ace at 8-7.
Karlovic, who won his first two ATP titles this year and earned a career-high ranking of No. 25 this week, will play either Tommy Haas or Juan Monaco in Saturday's semifinals at the Royal Tennis Hall.
Karlovic, at 2.08 meters (6-foot-10) the tallest player on the ATP tour, had 30 aces for a tour-leading 1,093 this year. Goran Ivanisevic set the record in 1996 with 1,477 aces.
Karlovic lost only four points with his serve in the first set, when his first-serve percentage was 88 percent.
Clement saved two break points in the second set at 1-1, and then broke Karlovic for the only time in the match to lead 4-3 when the Croat's forehand sailed long.
There were no service breaks in the third set.