Karlovic, who was given a bye into the second round, put up the kind of serving performance one has become accustomed to, firing down aces and not providing a single break point opportunity.
Despite this it was local favourite Galan who took the early advantage after edging a lengthy tie-break in the first set. Losing the opener appeared to galvanize Karlovic, who took control of the next two sets, winning 12 of the next 16 games.
Next up for Karlovic is a clash with wild card Radek Stepanek who defeated sixth seed Sam Groth on Wednesday.
Second seed Bernard Tomic was also under the cosh early on before recovering to beat Spaniard Adrian Menendez-Maceiras 6-7 (5-7), 6-2, 6-4.
The Australian is enduring something of a tumultuous time of it at the moment, having been arrested in Miami last week after an incident at a hotel, while his on-going feud with Tennis Australia shows no signs of letting up. However, he was able to put this to one side sufficiently to see off Menendez-Maceiras in an hour and 55 minutes.
Tomic will now face Tatsuma Ito in the quarter-finals after Ito kept the flag flying for Japan by beating Colombian Alejandro Gomez 6-1, 5-7, 6-0.
Third seed Adrian Mannarino navigated through a potentially tricky encounter with Rajeev Ram, the winner at the Hall of Fame Championships last week. The Frenchman made no mistake though, downing Ram 7-5, 6-3.
Yuichi Sugita of Japan gave fourth seed Victor Estrella Burgos a scared before the man from the Dominican Republic found his range when it mattered to record a 6-4, 6-7 (4-7), 6-2 victory.
Other winners on the day where seventh seed Malek Jaziri of Tunisia who defeated American qualifier Alexander Sarkissian 6-7 (1-7), 6-3, 6-2 to set up a clash with Mannarino, and Germany's Michael Berrer, who saw off Marcelo Demoliner of Brazil 6-3, 7-6 (7-3).