Andrus hit a tiebreaking, two-run double in the seventh inning after earlier ending a 1-for-18 slump. And his team beat the Red Sox 3-2 on Wednesday night one day after getting thumped by Boston 17-5.
"It was a huge win for us," Andrus said. "We're really good trying to turn the page and be ready for the next game. That's the way we've had success so far the last couple of years."
He went 2 for 4 in the meeting of the AL's top two teams. He singled in the fifth, and hopes the hitting will carry over for a while.
"You can't get (frustrated)," said Andrus, whose batting average has dropped from .282 to .261 in his last 14 games. "I know I haven't found my swing so far this year, but, at some point, it will get back. So I'm really glad just to do something for the team to get a win."
The victory gave the Rangers their best record through the first 58 games at 36-22 -- their previous best was 35-23 three times in the 1990s. They also broke a four-game road losing streak.
Texas has the best record in the AL, while Boston is second at 36-24 after its three-game winning streak was stopped.
The Rangers also got a big lift from Alexi Ogando, who returned after being on the disabled list since May 16 with a strained right biceps. He allowed one run on three hits in 5 2/3 innings and left after allowing Dustin Pedroia's tying homer with two outs in the sixth.
"To be out two weeks and to get a rehab start and throw 60 pitches," Texas manager Ron Washington said, "and then come against that lineup that showed what their might is about last night and shut them down like that, he deserves a lot of credit. It was a lift for us. We needed it."
Five Texas pitchers allowed Boston just five hits one day after the Red Sox got 19, including 13 for extra bases, in the opener of the three-game series.
John Lackey, sidelined all last season after Tommy John elbow surgery, gave up one run -- Adrian Beltre's 12th homer of the season in the fourth -- and five hits in six innings. He lowered his ERA from 2.96 to 2.79.
"I'm definitely taking some positives out of it," he said. "I think I'll take giving up one run for the rest of the way,"
His catcher was impressed.
"I thought he threw the ball great. Velocity was really up there," Saltalamacchia said. "There was a couple times where the ball was actually hurting my hand. He was able to throw that ball over the plate."
In the fifth, Andrus singled off Lackey then got the big hit on the first pitch from reliever Koji Uehara, his teammate in Texas the past two seasons.
"Elvis usually does that type of stuff," Washington said. "It seems like when he's in those types of situations where the team needed a lift and he's up there he finds a way to come through. We've known Koji for quite a while. He was with us and (Andrus) didn't waste any time. He jumped on his first pitch. He knows Koji likes to throw strikes and he jumped on it."
Breslow had relieved Lackey to start the seventh and allowed a leadoff double to Mitch Moreland, who left the game with tightness in his right hamstring and was replaced by pinch-runner Jeff Baker. After Jurickson Profar grounded out, pinch-hitter Craig Gentry walked and Uehara replaced Breslow to face Andrus, who broke the 1-1 tie.
Boston threatened with no outs in the seventh when Stephen Drew led off with a walk and went to second on a single by Jose Iglesias. After Jackie Bradley Jr. struck out, both runners advanced on a wild pitch. But Daniel Nava grounded out and Jonny Gomes flied out.
Saltalamacchia's double in the eighth drove in Mike Napoli, who walked with two outs.
Moreland said he would return to Texas for an MRI and hoped to be back for Thursday night's game. ... Lackey didn't get a decision for the first time in his nine starts. He allowed three runs or less for the eighth time this season. ... Iglesias reached base for the 17th time in his 18 games. ... To make room for Ogando, the Rangers sent LHP Joseph Ortiz to Triple-A Round Rock. Ortiz allowed six runs in 2 1/3 innings in Boston's win on Tuesday night. ... Derek Holland (5-2) pitches for Texas against Jon Lester (6-2) on Thursday night.