The 17-times grand slam winner, preparing for Wimbledon's grass courts, got his first break when Gulbis sent a forehand long to go 4-2 up. He easily held serve to bag the first set.
The pair traded blows in the second set before Federer again broke Gulbis with the world number 86 double faulting at 5-5.
The defending champion, who has won the tournament seven times, fired a forehand winner on his first match point to set up a quarter-final meeting with the German.
Czech Tomas Berdych, the third seed, also advanced, beating Croatian teenager Borna Coric in straight sets, losing just two points on his first serve in the entire match.
Ivo Karlovic also booked a last eight spot with a 6-7(5) 6-3 6-3 victory over German Alexander Zverev.
Second seed Kei Nishikori is in action on Thursday against Dustin Brown.
(Reporting by Karolos Grohmann; editing by Toby Davis)
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