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After about 2,000 feet worth of home runs left Sunday’s game tied, the Twins scored the winning run with about an inch to spare.

Brian Dozier, Max Kepler and Eddie Rosario all hit home runs, Jose Berrios recovered from a two-homer first inning to earn his 10th victory and the Twins rallied from a five-run deficit to beat Texas 6-5 and salvage a series split. But the decisive run almost didn’t count.

Robbie Grossman drove a single off the right-field wall with two outs in the fifth inning, and Eduardo Escobar headed home from second base. Grossman decided to try to stretch his hit into a double, though, and was thrown out on a close play — almost simultaneous with the moment Escobar touched the plate. Had Escobar taken a split-second longer to reach home, his run would have been disallowed; umpires consulted replay to confirm the bang-bang timing.

“It was a little bit of a mistake that [Escobar] made it so close. It’s one of those things that shouldn’t happen at this level,” Twins manager Paul Molitor said. “We almost got caught there, but we were able to get the run.”

And one run was enough, thanks to a suddenly sturdy Twins bullpen, anchored by a new 37-year-old closer. Twins relievers gave up only one run over 12⅔ innings during the four-game series, an impressive run for a unit that traded away its most reliable arm a week ago. Matt Belisle — who earned the sixth save of his 14-year career and first since 2012 — said the absence of All-Star Brandon Kintzler hasn’t shaken the remaining relief corps.

“I don’t think there’s any relent in this clubhouse,” Belisle said after his 1-2-3 ninth helped pull the Twins within 3½ games of an AL wild card. “We’ve been tremendous at unhooking the trailer of yesterday.”

Berrios was tremendous at “unhooking the trailer” of a lousy first inning, the Twins’ third in as many days. After a single and a one-out walk, Adrian Beltre recovered from an 0-2 count to clobber a fastball into the left-field seats, the first homer off Berrios in exactly a month. Two batters later, Joey Gallo crushed another Berrios mistake about 440 feet onto the right-field plaza, reminiscent of his memorable blast that shattered the windshield of a pickup truck on display at the Futures Game in this ballpark three years ago.

Molitor and pitching coach Neil Allen approached Berrios in the dugout and urged him to forget his rough start, and the manager was impressed with how he responded: four shutout innings, interrupted by a brief shower that led to a half-hour delay.

“We’ve seen him grow in a lot of ways this year. It’s been a lot of positive steps,” Molitor said of the 23-year-old. “We talked to him about, those are the kind of games where people step up and find a way to put some zeros up even though their pitch count is going to limit how far they can go. Try to give your team a chance to get back into the game. … He responded to that challenge very well.”

So did the Twins offense, which had been held to 29 hits over the previous five games. Kepler, who hadn’t homered since July 3, knocked a two-run shot in the second inning, and after the rain passed, so did Dozier, who became the ninth Twin to hit 20 home runs in four consecutive seasons. When Rosario, in the cleanup spot for the first time in his career, pulled one into the seats off Nick Martinez in the third inning, the deficit had disappeared — and the bullpen made sure it stayed that way.

“To be honest, it’s a little tricky right now,” Molitor said of protecting leads. Trevor Hildenberger pitched two shutout innings, and Taylor Rogers had a perfect eighth, the lefthander’s first scoreless outing in seven appearances. “A nice clean outing,” Molitor said. “I know he’s been searching for that for a while.”

And Belisle finished it off. Some games might go Rogers-Belisle, Molitor said, and some might be Belisle-Rogers, but “that’s the way we’re going to go. It might get flipped every now and then, but we’ve got enough experience” to survive the absence of Kintzler.

Twins 6, Texas 5 Monday:  vs. Milwaukee, 7:10 p.m. (FSN)