The 26-year-old Darvish carried over a strong showing in spring training this year into near perfection in his first regular-season start. The Astros looked totally lost against him, often taking wild swings at breaking balls that bounced.
With the crowd on its feet and a mixture of cheers and "Yuuus" filling Minute Maid Park, Chris Carter took Darvish to a full count before striking out on the ninth pitch of the at-bat for the first out of the eighth inning.
Rick Ankiel followed by striking out and Justin Maxwell hit an easy grounder to second baseman Ian Kinsler.
Darvish looked toward the sky for a couple of seconds before retreating to the dugout.
He began the ninth by getting two easy groundouts before Gonzalez ruined his bid. The 24-year-old Gonzalez made his big league debut last year, hitting .234 in 80 games for Houston.
Darvish, who played seven professional seasons in Japan before joining the Rangers, set rookie franchise records for wins and strikeouts last season. He finished third in AL Rookie of the Year voting behind winner Mike Trout and Oakland outfielder Yoenis Cespedes.
The win gives Darvish five straight regular-season victories dating to last season. He took the loss in the Rangers' 5-1 loss to Baltimore in the AL wild-card game.
Using his dizzying array of pitches, including a fastball that topped out at 97 mph, a slider, and 95 mph cutters, Darvish bedeviled the mostly inexperienced Houston hitters.
Darvish (1-0) sailed through the first four innings, striking out nine, including the side in the second and fourth.
Carter hit a long fly that looked as though it could be gone before David Murphy caught it just in front of the left-center wall for the first out of the fifth.
"I really thought it was a home run," Darvish said.
Michael Kirkman relieved Darvish after Gonzalez's hit. Jose Altuve followed with a single before Kirkman fanned pinch-hitter J.D. Martinez to end it.
Darvish has never thrown a complete game in the majors.
Lucas Harrell (0-1) allowed six hits and one run with four strikeouts in six innings for Houston.
Lance Berkman had a run-scoring single in the third against his former team. Kinsler hit a two-run homer off Rhiner Cruz in the seventh to make it 3-0. Texas added two runs in the eighth and two in the ninth.
NOTES: The last no-hitter by a Rangers pitcher was Kenny Rogers' perfect game against the Angels on July 28, 1994. ... These teams wrap up the series Wednesday when Humber makes his Astros debut against Texas RHP Alexi Ogando.