Chile's Gonzalez won 6-4, 4-6, 6-4 to set up a final eight meeting with Horacio Zeballos. The sixth-seeded Argentine swept past Israel's Dudi Sela 6-3, 6-2.
American John Isner was the main casualty of Thursday's play, with the towering second seed eliminated by Belgian veteran Xavier Malisse 7-6 (3), 6-7 (7), 7-6 (3).
Malisse's quarterfinal opponent will be American Wayne Odesnik, who was a 6-1, 7-5 winner over Kazakhstan's Mikhail Kukushkin.
While Isner departed, another big-serving American, Sam Querrey, blasted his way through with a 6-2, 6-1 win over Slovenia's Blaz Kavcic. Querrey will take on Chile's Nicolas Massu next.
Fourth-seeded Australian Lleyton Hewitt started understandably poorly in his return from injury but fought back to beat India's Somdev Devvarman 1-6, 6-0, 7-6 (2).
Hewitt will face old rival Juan Ignacio Chela of Argentina in the quarterfinals.
In Marbella, Spain, top-seeded Victoria Azarenka of Belarus retired from the quarterfinals of the Andalucia Open on Friday because of a leg injury while leading 4-0 against fifth-seeded Maria Jose Martinez of Spain.
Azarenka received treatment on court to her left leg but was not able to continue.
Second-seeded Flavia Pennetta of Italy beat Romanian qualifier Simona Halep 6-4, 7-6 (4), and eighth-seeded Carla Suarez Navarro of Spain rallied to beat Tatjana Malek of Germany 4-6, 6-1, 6-2.
In Casablanca, Morocco, Stanislas Wawrinka of Switzerland and Potito Starace of Italy won in straight sets Friday to reach the semifinals of the Grand Prix Hassan II.
The top-seeded Wawrinka beat Moroccan wild card Reda El Amrani 6-3, 6-1 and will next play Starace, who upset fourth-seeded Lukasz Kubot of Poland 6-1, 6-0.
It will be Starace's first ATP tour semifinal since 2008 at Kitzbuhel, Austria.
Wawrinka won six straight games to clinch the match, without allowing a break chance to El Amrani.
In the opening set, Starace broke Kubot twice and then saved three break points to lead 5-0. Kubot won only four points on serve in the second set.
Last year's runner-up, Florent Serra of France, also advanced by defeating Guillermo Garcia-Lopez of Spain 6-2, 6-2.
Serra broke the second-seeded Garcia-Lopez twice in each set and will take on Victor Hanescu of Romania or Richard Gasquet of France.
