The Latvian was taken the distance by the 17-time grand slam winner but held his nerve in the decider to record a 6-7 (5-7) 7-6 (7-3) 6-2 4-6 6-3 victory.
Gulbis will now face Tomas Berdych in the second grand slam quarter-final of his career, and he hopes his good record in France will inspire him to an unlikely triumph at Roland Garros.
“It’s the biggest win of my career,” said the world number 17. “Sorry I had to win. I know how everyone likes Roger.
“It was a tough match but this is sport.
“I’ve been playing very well in France. I won tournaments in Marseille and Nice, hopefully Paris is the next one.”
The win was Gulbis’ second over Federer in their four meetings, but the first at a grand slam event.
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