Stone Garrett and Dominic Smith also homered for last-place Washington, which won the final two games of the series after dropping 15 of its previous 16 at Nationals Park.
“Hats off to the group to come back against a first-place team like that and to take a series going into the (All-Star) break," Smith said. "I think we can build on that and there's a lot of things we can look forward to in the second half.”
Texas enters the break atop the AL West despite losing eight of its past 11. The Rangers (52-39) have not won a series since taking two of three June 19-21 from the Chicago White Sox, but still are tied for their fifth-best record through 91 games in franchise history.
Texas just completed a stretch of 30 games in 31 days, including 17 in a row ending Sunday.
“You take where we're at at the break,” Texas manager Bruce Bochy said. “Do we like how it's gone the last couple weeks? No, this is not how we want to finish. There's challenges during the course of a season and every club goes through them. ... I will say I think the break is coming at a good time. This has been a tough part of the schedule.”
Meneses has batted third or fourth most of the season for Washington after hitting 13 homers in 56 games last season. But he had only two in his first 80 games this season before going deep twice Friday and once more Saturday.
He added another Sunday, taking reliever Josh Sborz to right-center in the seventh. It is the second time in his career Meneses has homered in three consecutive games.
“He's starting to understand how to use his legs again,” Washington manager Dave Martinez said. “Hopefully, he has a monster second half for us.”
Corbin (6-10) matched his victory total from all of last year, when he led the majors with 19 losses. He retired the first 10 men he faced and allowed one run and five hits while striking out six over seven innings.
“Early, he really had that slider going well along the fastball and he used them both effectively and commanded them," Bochy said. “We expanded (the zone) going after the slider down, which is unlike us. But he was on top of his game today.”
Smith hit Texas starter Dane Dunning's first pitch of the fifth inning to right-center to open the scoring. Lane Thomas added an RBI single later in the inning.
Dunning left with two men on in the sixth, and Sborz allowed Luis García's infield single to load the bases. Alex Call followed with a two-run single, and CJ Abrams added a run-scoring single to make it 5-1.
Garrett homered two batters after Meneses' shot in the seventh to end Sborz's outing.
Dunning (8-2), one of Washington's first-round picks in 2016, pitched for the first time at Nationals Park and allowed four runs in 5 2/3 innings. The right-hander allowed seven hits while striking out four.
Adolis García drove in both of the Rangers' runs, on a bloop single in the sixth and a force out in the eighth.
Rangers: Texas has not revealed its rotation for when it returns home Friday to open a three-game series against Cleveland.
Nationals: Washington has not announced its pitching plans for after the All-Star break. The Nationals begin a three-game series Friday at St. Louis.
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