The slugger's sharp single to right with two outs in the ninth ended the game, giving the Rangers a 7-6 victory Thursday night and a split in the four-game series against the AL East-leading New York Yankees.
"Playing the Yankees is always fun, the battle back and forth between teams and between fans in the stadium," said Hamilton, who had the three-run homer in the first inning. "It's always good to have that win."
His RBI single wrapped up a wild ninth in a game that started at 101 degrees, the hottest for a major league game this season, and ended under a full moon with the temperature still in the low 90s.
Yankees starter CC Sabathia was taken to the hospital with symptoms of dehydration after coming out one batter into the sixth inning. He threw 80 pitches.
A Yankees spokesman said after the game that Sabathia showed no symptoms of dehydration during the game, but was sent to the Medical Center of Arlington after cramping while icing in the trainer's room after coming out. The team provided no other update.
Delino DeShields drew a leadoff walk in the ninth off Nick Goody, who was making his major league debut. Yankees closer Andrew Miller (0-2) got Elvis Andrus out on a deep fly ball before DeShields became the second out when he was hit on the foot by Leonys Martin's hard shot while running the bases.
The Rangers played the night before the non-waiver trade deadline while waiting for the completion of an expected deal to acquire ace left-hander Cole Hamels and a reliever from Philadelphia for Matt Harrison and a package of top prospects.
Rangers officials said during the game that there would be no announcement Thursday night.
Teixeira has 26 homers this season after the 40th multihomer game of his career, and third this season. But he struck out in the ninth against Shawn Tolleson (3-2), the Texas closer pitching in a non-save situation.
Rua hit a sinking liner that bounced over the glove of diving center fielder Jacoby Ellsbury and rolled to the wall in the fourth, tying the game 5-all.
"That was fun to watch," manager Jeff Banister said. "It's one of the more fun plays in baseball when you're on the positive side of that. ... I think everybody in the ballpark was yelling for him to go."
Yovani Gallardo, the Rangers' right-hander who has been mentioned as a possible trade target for other contending teams, allowed five runs over six innings. He has given up 15 runs over 14 innings in his last three starts, after an earlier stretch this season with 33 1/3 consecutive scoreless innings over a span of six games.
Sabathia gave up five runs -- all scoring on the three homers -- while pitching through the leadoff batter in the sixth. He has allowed 24 homers, most in the American League.
"It looked like he would get out of the first, but then he hung a slider to Hamilton," manager Joe Girardi said. "That was the one big hit that hurt us."
Sabathia was moved up a day in the rotation to start after Michael Pineda was put on the disabled list earlier in the day with a right flexor forearm muscle strain. The DL move was retroactive to July 25, the day after his last start.
GIVE HIM THREE
Jacoby Ellsbury led off the game with a triple, a play that was originally ruled a double and an error on Ryan Rua before it was determined that the ball got past the left fielder only after taking an awkward hop off a sprinkler head. Brett Gardner immediately followed with a sacrifice fly.
Yankees: An MRI on Pineda's forearm showed no structural damage. When asked where he felt pain, he pointed to a spot a few inches below his right elbow.
Rangers: LHP Derek Holland threw 39 pitches in 1 2/3 innings for Triple-A Round Rock in the first start of his injury rehab.
Yankees: New York opens a three-game series against the Chicago White Sox on Friday. That is the final series in the Yankees' 10-game road trip that matches the season's longest.
Rangers: For the first time since the 2010 World Series, the Rangers host the San Francisco Giants. The Giants played at Texas for MLB's first-ever interleague game on June 12, 1997, but haven't played a regular-season game there since 2001.
- Home Plate Umpire - Paul Emmel
- First Base Umpire - Jerry Meals
- Second Base Umpire - Andy Fletcher
- Third Base Umpire - Jordan Baker