Fifth-seeded Fernando Verdasco of Spain, German qualifier Philipp Petzschner and Carlos Moya of Spain also reached the quarterfinals. No. 3 Juan Martin del Potro and No. 8 Gael Monfils won their opening matches.
Gulbis nearly ended Gonzalez's bid for at least a fourth straight appearance in the past eight in Vienna.
He broke Gonzalez in the 10th game for the first set, and had five match points on the second seed from Chile in the second-set tiebreaker. But he netted a volley and hit two returns long while Gonzalez produced two forehand winners. Gulbis double-faulted on set point for Gonzalez.
"It was difficult to get into the match because he was hitting the balls so hard,'' Gonzalez said. "I was too slow. He was in control of the match and hit winners all the time.''
Gonzalez got an early break to go up 3-0 in the third set, and another break sealed the victory for the 2006 finalist.
"I didn't score a lot on my serve, so I had to fight for every single point,'' Gonzalez said. "I am not playing my best tennis, so it's great to have two wins.''
Verdasco won the last six games to beat Guillermo Canas of Argentina 6-1, 6-2 and make his seventh quarterfinal of the year.
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.
In the quarterfinals, Petzschner will play Moya, who defeated Eduardo Schwank of Argentina 6-2, 6-3.
Moya hit nine aces and held off all five break points against his serve. He broke Schwank three times.
In first-round play, del Potro of Argentina defeated Martin Fischer of Austria 7-6 (7), 7-6 (5).
The 219th-ranked Fischer missed a set point in the first-set tiebreaker and went a break up in the second, but del Potro came back and converted his third match point.
"I was very tired but I am close to qualifying for (the Masters Cup in) Shanghai so that keeps me going,'' del Potro said. "He played well but had too many mistakes on the important points. That made the difference.''
Del Potro, who won four tournaments in a row this season and lost the final of the Japan Open on Sunday, next plays Philipp Kohlschreiber for a place in the quarterfinals.
Monfils beat Alexander Peya of Austria 3-6, 6-1, 6-3. The Frenchman was 3-1 down in the opening set when he slipped behind the baseline and smacked the back of his head on the court. He was treated for a painful neck twice and lost the first set, but dominated the match afterward.
Gonzalez saves 5 match points against Gulbis
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