With the A's also winning, the Rangers stayed 1 1/2 games back of them for the top spot in the American League West.
"It was a very important win for us; we needed it bad," Rangers manager Ron Washington said. "We went out there, got on the board first, fought back, didn't give in and made things happen."
The Rangers' big inning came in the seventh, when a walk to Leonys Martin and a ground-rule double by Ian Kinsler put runners on second and third with one out. A sacrifice fly by Elvis Andrus and a double by Alex Rios then gave Texas a 4-3 lead.
"Made a bad pitch to Kinsler; that's pretty much all I did," Angels reliever Michael Kohn said. "Other than that, I thought I threw the ball well, got Andrus to pop up. Infield obviously playing in in that situation, and Kole Calhoun made an unbelievable catch. Then Rios, got in on his hands pretty good, and he dumps it in to short center field."
Left-hander Neal Cotts made things interesting in the eighth, when Calhoun led off with a double. Yet, Cotts was replaced by right-hander Tanner Scheppers, who got Mark Trumbo to ground out and Hank Conger to strike out. Scheppers then got Grant Green to fly out to center field and end the inning.
"I thought that was outstanding: He came in, and with that runner at third I kept thinking how we really needed a strikeout, and he did it," Washington said. "That was a great inning; we needed that. He came in throwing strikes."
Scheppers acknowledged after the game that it was a huge situation.
"I don't ever try to look for the strikeout," Scheppers said. "I wanted to get a soft ground ball, something where he couldn't get extended."
The Rangers used six relievers, who allowed just one run on five hits in 5 2/3 innings.
Right-hander Nick Tepesch made his first start since July 5, tossing 3 1/3 innings and allowing two runs on four hits for the no-decision. Tepesch tossed 63 pitches, 41 of which were strikes.
"We knew Nick would be on a short pitch count, and all of the pitchers stepped up," Washington said. "We came back and kept fighting."
Tepesch got out of a jam in the first after giving up a base hit, and then a walk to Mike Trout with one out. However, he was able to get Josh Hamilton to ground into a double play and end the threat.
He was not as lucky in the second, surrendering a leadoff home run to Calhoun to tie the score at 1. In the three-hole with the Rangers for the first time this season, Rios had belted a solo home run off Angels starter Jason Vargas in the first inning.
"I was very pleased with his performance today," Washington said of Rios. "He got us on the board early and then got a big double at the end to drive in a run. He did a lot of good things today. It worked."
Tepesch was pulled after allowing a single to Trumbo with one out in the fourth. He made way for reliever Joseph Ortiz, who proceeded to give up a double to Conger and later a two-run double to Angels third baseman Andrew Romine, which gave the Angels a 3-1 lead.
However, the Rangers would get a run back when Andrus hit an RBI single that scored Martin in the next inning.
Fighting back every time the Angels scored a run, the Rangers' gritty, resilient win will stay with the team as it heads back to Arlington to begin a six-game homestand against the Pirates and A's.
"Right now every win is important; we are playing for the pennant," Rios said. "What we did today in coming from behind was great. Hopefully it will boost out confidence and keep us going."