Murray needed five sets to beat Radek Stepanek and Mathias Bourgue, but the second seed took only an hour and 58 minutes to see off Karlovic 6-1 6-4 7-6 (7-3) on Court Suzanne-Lenglen.
Two-time grand-slam champion Murray teetered on the brink of a Roland Garros exit in his first two matches, but the Brit coasted to a seventh victory out of seven against the lofty Croatian on Friday.
Karlovic came through a gruelling five-setter against Jordan Thompson to become the oldest player to reach round three of a grand slam in 25 years, but that appeared to have taken its toll on the big-serving 37-year-old.
It was Murray's serve that proved to be more potent as he did not face a solitary break point and stayed in the hunt for a first French Open title, with John Isner or Teymuraz Gabashvili awaiting in the last 16.
World number two Murray made a blistering start, breaking by lifting a perfectly executed lob over the imposing frame of Karlovic to take a 2-0 lead.
Karlovic was unable to wind up his vicious serve and two double faults gifted Murray another break point, which he won with a fizzing forehand that the veteran was unable to return.
Murray served out the set to love after a stiff-looking Karlovic finally got on the board and the Scotsman carried on where he left off with a break in the opening game of the second set, forcing another error from his out-of-sorts opponent.
The world number 28 was given a let-off when Murray was unable to put away a forehand pass for a 4-1 lead after earning two break points, but the favourite was soon sitting down with a two-set lead.
Karlovic dug deep to save two break points in the fifth game of a third set which went with serve, but Murray claimed two mini-breaks in the tie-break with sublime winners and advanced when the 27th seed fired a forehand long.