In the bottom of the 10th, former Ranger Ivan Rodriguez hit a double off Nick Regilio (1-2) and scored on Craig Monroe's single, giving Detroit a 6-5 win.
"It was a very tough game," Mark Teixeira said. "We've got to win those games. You've got to give them credit. They fought back and they deserved to win at the end."
Former Tiger Andres Torres led off the game with a double down the left-field line off Detroit left-hander Nate Robertson. Michael Young followed with a single to center and Torres moved to third. The hit extended Young's hitting streak to 12 games, which ties his career high. Teixeira's base hit scored Torres. Young then scored on a fielding error by Detroit second baseman Omar Infante, making it 2-0 in favor of Texas.
Robertson didn't allow another hit until the fifth inning.
"We seemed to have more trouble with him in our park than we did here," Rangers manager Buck Showalter said. "But he changed his approach after the first inning. He probably threw five or six fastballs after the first inning. Everything was off-speed and they had a lot of success with it. Tip your hat to him and Pudge [Rodriguez], making the adjustment."
Detroit left fielder Rondell White got a run back in the top of the second, when he led off with a solo home run to left field off Texas starter Chris Young.
White again gave Young problems in the third inning. Speedy Nook Logan led off with an odd infield single between first base and the mound. Teixeira fielded the ball, and then collided with Young. Logan avoided the tag but replays showed that he missed first base. Brandon Inge walked. Infante's sacrifice moved the runners over and both scored on White's base hit to left field, and the Tigers led, 3-2.
"It was a tough play, he's a fast runner," Chris Young said. "I got in Teix's way. I didn't know where Logan was. It's my fault. He did not hit the bag, I know that for a fact. You can't let it affect you. You have to go and make the next pitch, get the next out."
The Rangers reclaimed the lead in the seventh. Sandy Alomar Jr. hit the ball to first baseman Chris Shelton, who threw the ball away. Alomar was credited with a single and took second on the error. Mark DeRosa, making his first start since May 16, got his second hit of the game and Alomar went to third.
Torres' sacrifice fly scored Alomar to tie the game at 3. After Franklyn German relieved Robertson, Young singled again for his fourth straight multi-hit game. Then Teixeira singled in DeRosa for a 4-3 Texas lead. Kevin Mench's sacrifice fly made it 5-3.
Young allowed three runs on four hits while walking two and striking out a career-high eight.
In the eighth, Kameron Loe gave up a single to Inge and hit Infante with a pitch, forcing Showalter to go to Cordero early. Cordero got the final two outs.
"We're trying to develop a 23-year-old guy out of the bullpen," Showalter said of Loe. "The good ones learn from it."
Then in the ninth, Monroe and Shelton singled off Cordero. Rookie Tony Giarratano walked after trying to bunt, loading the bases. Carlos Guillen got a pinch-hit sacrifice fly to score one run and Infante hit a single to score another and tie the game.
"I've got to do my job," Cordero said. "They're a pretty good hitting team. They got on base, the one guy was bunting and I walked him. I've got to make my pitches."
Detroit won the season series, 4-2. It is the earliest the Rangers have ever completed a season series against an American League foe.
Dana Wakiji is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.