"I did tell the coaches that I wasn't feeling good," Darvish said through a translator. "I could have gone six or seven innings. In the end, the manager made the decision to stop me."
Darvish (7-2) breezed through the first two innings, but gave up single runs in each of the next three innings and was pulled. He threw 93 pitches on a 91-degree day, allowing seven hits and walking three to win his 100th combined game in Japan and the United States.
"I'm not looking at it as an injury," Darvish said. "I feel comfortable saying that I should be able to treat this and be ready for my next start."
In his previous outing, he allowed five runs and walked a career-high six in four innings against Seattle.
The AL West leaders outscored the Blue Jays 34-16 in the series, extending Toronto's losing streak to five games. J.P. Arencibia hit two solo home runs for the Blue Jays.
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"It's always been a terrific lineup," Texas manager Ron Washington said. "We have All-Stars. The guys who hit behind
Kyle Drabek (4-5) allowed a career-high nine runs in three innings and lost for the second time this season to Darvish.
"We needed a win and I just wasn't there for the team," Drabek said.
Toronto pitchers had a 7.81 ERA on a 1-5 road trip that included a stop at Tampa Bay. Blue Jays relievers threw 18 2-3 innings in the Texas series.
"We had some momentum going into this road trip," Toronto manager John Farrell said. "We ran up against two really good teams."
Colby Rasmus had three hits, including a two-run homer in the ninth for the Blue Jays. Toronto last lost five in a row during the middle of the 2010 season.
The Rangers sent 11 batters to the plate and had five hits in the big second. Drabek gave up a single to Young and walked two to load the bases with one out, and a walk to Mitch Moreland forced home a run. Kinsler and Elvis Andrus hit two-run doubles and Beltre capped the burst with his 10th home run.
It was the fourth time this season the Rangers have scored seven or more runs in an inning.
Kinsler's two-run homer in the fourth made it 9-1.
"Their starting pitcher is good so it was nice to get runs early," Young said. "It was a big lift for us."
- Toronto SS Yunel Escobar left the game in the fifth with tightness in his left groin.
- The Rangers had their 16th home sellout. The team passed the 1 million mark in attendance in its 23rd home game, the fastest the club has hit that mark.
- Toronto RHP Jesse Chavez, whose contract was selected from Triple-A Las Vegas before Sunday's game, pitched the final five innings and gave up three runs.