The eighth-seeded Frenchman will next play Philipp Kohlschreiber of Germany, who defeated No. 5 Fernando Verdasco of Spain 6-2, 6-3.
"I am very happy because I was focused from the first ball to the last,'' said Monfils, who reached his fourth semifinal of the year. "I tried to be aggressive because he (Gonzalez) is a fighter who becomes dangerous if you let him play.''
Gonzalez, who lost the 2006 final to Ivan Ljubicic, was in his third quarterfinal match in as many weeks.
From 3-3 and 0-15 in the opening set, Monfils won 12 straight points to close it out. The second set went with serve until 5-5 when Monfils converted his first break point.
Monfils failed to serve out the match, but went up 6-0 in the tiebreaker and finally converted his third match point when Gonzalez netted a forehand.
Kohlschreiber earned his third semifinal appearance of the season - he won in Auckland, New Zealand, and reached the final in Halle, Germany.
The 32nd-ranked German conceded only 10 points on his serve and didn't face a break point. He had two breaks against Verdasco's serve in each set.
Mijatovic: Keep Up The Rotation, Bernd
Gonzalez saves 5 match points against Gulbis
WC Debate: Who Are The Greatest-Ever World Cup Nation?
