Sabathia, moved up a day in the rotation to start after Michael Pineda was put on the disabled list earlier in the day, threw 80 pitches through one batter in the sixth inning.
A Yankees spokesman said postgame 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 being taken out. The team provided no other update.
''I felt good. It was just one of those days,'' Miller said. ''Both of the outs I got were two of the hardest-hit balls I've given up this season.''
Delino DeShields drew a leadoff walk in the ninth off Nick Goody, who was making his major league debut. Miller got Elvis Andrus 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.
Martin went to second on Adrian Beltre's walk before the single by Hamilton, who also had a three-run homer in the first.
''He got behind in the count. He had a walk in that inning. He hasn't had a lot of work,'' manager Joe Girardi said of Miller.
The 101-degree start was the hottest this season in the majors. Even as a full moon rose over the field, the temperature was still in the low 90s when the game ended.
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,'' Girardi said. ''That was the one big hit that hurt us.''
Pineda has a right flexor forearm muscle strain and the DL move was retroactive to July 25, the day after his last start. Even though Sabathia was pushed up a day from his scheduled start Friday, he was pitching on normal rest since the Yankees used a spot starter earlier in this series.
Teixeira has 26 homers this season after the 40th multihomer game of his career, and third this year. But he struck out in the ninth against Shawn Tolleson (3-2), the Texas closer pitching in a non-save situation.
Texas had three homers, including Shin-Soo Choo's solo shot and Ryan Rua's inside-the-parker.
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.''
Yankees reliever Dellin Betances hasn't allowed an earned run in his last 29 road appearances since last Aug. 28, the second-longest streak by a Yankees pitcher since at least 1914. Mariano Rivera had a 37-game stretch from August 2004 to August 2005. Texas loaded the bases against Betances in the seventh before he struck out pinch-hitter Mitch Moreland to end the inning. The right-hander then struck out the first two batters in the eighth before being relieved.
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.
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.