Kinsler became the fourth player in Rangers history with a cycle, reaching the feat with a triple in the sixth inning. With his RBI double in the eighth, he became only the second Texas player with a six-hit game and then scored his fifth run, matching another team record.
Nelson Cruz matched the AL home run lead with his fifth homer -- a grand slam off reliever Radhames Liz that gave the Rangers a 10-3 lead. That accounted for half of the eight unearned runs Texas scored in the fourth, when Kinsler had two singles.
Kinsler led off the first with a double and hit his third homer of the season in the third.
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Kris Benson (1-1), who missed the last two seasons after surgery to repair a torn right rotator cuff, hadn't won since Sept. 21, 2006, when he was pitching for Baltimore against Detroit. The right-hander allowed four runs in six innings.
Marlon Byrd had went 5-for-6 with three RBIs for the Rangers, who had 19 hits. Their 19 runs are the most scored in the majors this season, and the most for them since their 30-3 victory in Baltimore on Aug. 22, 2007.
Cruz came only a few feet from hitting another grand slam, his flyball in the eighth hitting about halfway up the 14-foot wall in left field for a two-run double.
Baltimore, which still has won its first three series in a season for the first time in 11 years, jumped out to a 2-0 lead on consecutive RBI groundouts in the first after Benson walked leadoff hitter Brian Roberts and allowed a double to Adam Jones.
Luke Scott led off the Orioles second with a double and scored when Jones drew a bases-loaded walk for a 3-1 lead.
Only two of the nine runs allowed by Orioles starter Mark Hendrickson (1-1) were earned. The left-hander allowed seven hits and walked four in 3 2-3 innings.
After Kinsler's solo homer, Michael Young reached on shortstop Cesar Izturis' fielding error and scored on Hank Blalock's single that rolled under the glove of second baseman Brian Roberts. Marlon Byrd followed with an RBI double that broke the 3-3 tie and put Texas ahead to stay.
Rookie Elvis Andrus, the No. 9 hitter, drew a leadoff walk in the fourth before Kinsler singled and Young reached on Roberts' throwing error that allowed a run. There were two outs when Byrd's RBI single made it 6-3 and chased Hendrickson.
Then came Liz, recalled Wednesday after third baseman Melvin Mora and right-hander Alfredo Simon were put on the disabled list. The right-hander gave up four runs in his one inning, including an RBI triple by Andrus.
Kinsler's triple came on a deep flyball into the right-center field gap. After Kinsler slid head-first into third, he got up and slapped his hands together.
It was the first cycle for the Rangers since Gary Matthews Jr., at Detroit on Sept. 13, 2006. The other Texas cycles were both against Cleveland, Mark Teixeira on Aug. 17, 2004; and Oddibe McDowell on July 23, 1985.
Alfonso Soriano had the only other six-hit game for Texas, against Detroit on May 8, 2004.
Notes:@ Baltimore has won the first two games in each of its series this season, only to lose the finale. ... Jones hit a two-run homer in the ninth. ... Josh Hamilton had only two strikeouts in his 31 at-bats before Wednesday, but struck out twice. ... Rangers RHP Willie Eyre, who missed last season while recover from ligament transplant surgery in his elbow, made his season debut with two scoreless innings. ... Benson signed a minor league deal with Texas a week into spring training and made the team.