The second-seeded Chilean lost the opening set when he dropped serve at 5-4 down.
"It was difficult to get into the match because he was hitting the balls so hard,'' Gonzalez said.
In the second-set tiebreaker, the 56th-ranked Gulbis had five chances to close out the match but netted a volley and hit two returns long while Gonzalez produced two forehand winners. Gulbis then double-faulted on set point for Gonzalez.
Gonzalez had an early break to go 3-0 up in the decider and added another break to seal the victory.
Fifth-seeded Fernando Verdasco of Spain and German qualifier Philipp Petzschner also reached the quarterfinals.
Verdasco, who is ranked 13th, beat Guillermo Canas of Argentina 6-1, 6-2. The Spaniard dictated the pace of the match from the baseline and dropped serve only once early in the second set, but won six straight games to wrap up the win.
Petzschner, who eliminated top-seeded Stanislas Wawrinka on Tuesday, defeated Jan Hernych of the Czech Republic 6-3, 6-4. Petzschner hit six aces and faced no break points against his serve.
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