He didn’t know for sure until the phone rang.

As the Twins prepared to bat in the eighth inning Sunday, Jared Burton watched bullpen coach Bobby Cuellar pick up the receiver, listen for a moment, then turn to him as he hung up. “He says, ‘Burton, you got it,” the veteran reliever recounted. “I said, ‘All right — let’s do it.’ ”

And so he did, needing only 12 pitches, nine of them strikes, to finish off the White Sox and the Twins’ first-ever four-game sweep in Target Field. Glen Perkins needed a day off after pitching in three straight games, so Burton — who didn’t know ahead of time that he would get the ninth inning — threw a breaking ball in the dirt that Conor Gillaspie chased, a high fastball that Dayan Viciedo missed, and fielded Alejandro De Aza’s surprise bunt himself for the final out of the Twins’ 6-5 victory, earning his first save in more than a year.

“They’re trying to get on base, so most of the time they’re going to take a strike in the ninth,” said Burton, whose last save came on May 30, 2013. “If you can get ahead 0-and-1 on every hitter, you’re going to be a lot better off.”

If Burton is returning to the form he showed a year ago, when the bullpen was the team’s strongest element, the Twins are going to be a lot better off, too. The bullpen ERA of 3.61 ranks fifth in the American League — and that includes a once-wobbly Burton.

He is still digging out of an awful first six weeks, when he gave up runs in half of his first 10 appearances and lost his eighth-inning job to Casey Fien. At 5.52, his ERA still isn’t healthy. But he is, finally, and his recovery might be one of the most important developments for the final 90 games.

Video (01:35): Burton didn't know he'd close Video (01:35): Burton didn't know he'd close

“I’m feeling good, man. It’s been a little inconsistent year, a frustrating year mentally and physically. But you have to stay on an even keel,” said Burton, 33. “I know that eventually, you’re going to get a little momentum and get on a roll.”

Looks like the Twins might have, too, and they can thank the schedule-maker for it. After a road trip that took them to visit two first-place teams and the reigning world champion — an Eastern trudge that ended miserably with five losses in a row — the AL provided the perfect rebound opponent. The White Sox are the most pleasant, reassuring guests — challenging, entertaining, but at the critical moments, accommodating, too.

The Twins, after all, fell behind early in all four games this weekend, but rallied to win all four, too, their longest streak of success this season. Joe Mauer drove in a pair of runs for the third time in the series, Hughes won his eighth game despite being roughed up for a five-run inning, and the Twins stretched their longest winning streak of the season to four games. They suddenly are just two games below .500 once more, and tied for third place in the AL Central.

Hughes (8-3) surrendered five singles and a double (and even more unlikely: a walk, breaking his 106-batter walk-free streak) in the third inning, but he gave up little else, and the bullpen did the rest, holding Chicago scoreless to preserve the Twins’ third one-run victory in four games.

Mauer singled twice off John Danks, his 22nd consecutive home game vs .the White Sox in which he has collected a hit, and both singles drove in runs. After managing only two multi-RBI games through his first 64 games, Mauer drove in two apiece in three games of this series.

Not since June 2-5, 2011, in Kansas City had the Twins swept a four-game set. And their last four-game sweep at home came in the Metrodome seven years ago: July 12-15, 2007, against Oakland.

Back then, Burton was just breaking into the majors, after spending a couple of seasons at Class A (Stockton) and AA (Midland) throwing to a catcher who also got to the big leagues: Kurt Suzuki.

“I called him Lights-Out Levi,” Suzuki said, using Burton’s real first name. “He’s just a big hoss and he comes right at you. … I just love seeing him on the mound.”