Third seed Federer found his way through Karlovic's booming serve and presence at the net to win 7-6 (8-6) 7-5 6-3 and set up a potential last-16 match with Australian teenager Bernard Tomic.
In their 10 previous encounters, the pair had played 13 tiebreaks and the routine continued in the first set on Friday.
The serve-for-serve pattern shifted when Karlovic won a rare baseline rally to give himself set point at 6-5 in the tiebreak with two of his own massive serves to come.
His first flew long after being fired down at 211km/h, enabling Federer to take advantage of the second serve, ultimately lobbing the 208cm Croatian to draw the tiebreak back to level terms.
Karlovic then tried again with another 211km/h first serve which Federer rifled straight back past him with a stinging backhand return to give himself set point, which he took with a service winner on the next point.
The second set looked headed for another tiebreak at 6-5 with Karlovic to serve, but four stunning backhand winners from Federer broke Karlovic for the first time to allow the Swiss to go two sets up.
Federer only needed one more break in the third set to secure the match and take a 10-1 head-to-head record against the world No.57.
The four-time Australian Open champion will face a fourth round match against the winner of Friday night's match between Tomic and Ukrainian Alexandr Dolgopolov.
