The game was delayed for 10 minutes in the top of the sixth when home plate umpire Kerwin Danley was hit on the head by a broken bat and had to leave the field on a stretcher.
The Rangers won on the road for the first time in four tries and have won back-to-back games after losing seven of their previous eight.
Halladay (3-1) gave up five runs and eight hits in eight innings, walking none and striking out nine. Five of the eight hits he surrendered were for extra bases.
In 20 career games against Texas, Halladay is 7-7 with a 5.36 ERA, his highest against any AL opponent. He lost his only start against the Rangers in 2008, giving up four runs and 11 hits in nine innings.
The winner was right-hander Brandon McCarthy (2-0), who gave up three runs and six hits in six innings. He walked two and struck out two.
Toronto scored a run in the eighth to make it 5-4 on shortstop Elvis Andrus' throwing error and Adam Lind's RBI single off reliever C.J. Wilson, then loaded the bases with one out but couldn't score.
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Closer Frank Francisco relieved after Lind's hit and gave up a single to Scott Rolen and a walk to Lyle Overbay. But Francisco got Rod Barajas to line sharply to third and Travis Snider flied out to center.
Aaron Hill doubled and went to third in the ninth but Francisco got Vernon Wells to fly out for his second save.
Danley was struck by the barrel of Texas designated hitter Hank Blalock's broken bat on an infield popup, knocking him to the ground. Hunter Wendelstedt moved from second base to home plate.
Danley was taken to hospital with a possible concussion but did not lose consciousness, according to the Blue Jays.
On April 26, 2008, Danley was taken off the field on a stretcher after being hit in the head by a pitch from Los Angeles Dodgers right-hander Brad Penny. He was released from the hospital the next day and returned to the field in June.
Danley also was knocked out of a June 2006 game between the Houston Astros and Chicago Cubs after being hit on the collarbone by a pitch.
Cruz's sixth homer of the year gave Texas a 2-0 lead in the second but Toronto tied it in the third on an RBI double by Rios and Wells' sacrifice fly.
Chris Davis' RBI single in the fourth made it 3-2 Texas but Hill tied it again with a homer in the fifth.
The Rangers went ahead to stay in the seventh when Kinsler hit a two-out homer to right, his fifth.
It was the second homer in as many games for Kinsler, who batted .556 (15-for-27) with two homers and six RBIs last week, splitting AL player of the week honors with Kansas City pitcher Zack Greinke.
Notes: Josh Hamilton snapped an 0-for-15 slump with a single in the eighth. ... Texas RHP Kris Benson has been pushed back three days because of elbow tendinitis and will next pitch Saturday at Baltimore. Left-hander Matt Harrison and right-handers Kevin Millwood and Vicente Padilla will all move up one day, with Harrison starting in Benson's place Wednesday at Toronto. ... Alcohol was banned at Rogers Centre again Tuesday, the second and final Blue Jays game affected by a ban from the Alcohol and Gaming Commission of Ontario. The Jays were banned after infractions at the stadium dating to November 2007. Alcohol was banned from Toronto's April 7 game against Detroit. An Aug. 1 Canadian Football League game will also be dry.