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.
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.