Voit made his third start out of the leadoff spot this year and was New York's designated hitter now that the team is comfortable playing Giancarlo Stanton in the outfield. He gave the Yankees a 3-0 lead with a double down the left-field line off John Gant (0-1) and then scored on a sacrifice fly by Anthony Rizzo - his replacement at first base.
"That what Luke's capable of," manager Aaron Boone said. "He's a really good hitter and came up in a big spot there and delivered."
Voit's clutch hit came two nights after he drove in the decisive runs in a doubleheader sweep of Boston and said he deserved to play as much as Rizzo. After scoring New York's fourth run on Rizzo's sacrifice fly, Voit emphatically clapped his hands after crossing the plate.
Voit's hit came in his sixth career start as a leadoff hitter. He flied out to the warning track to open the game but went on to continue his recent surge. He is batting .412 (7 for 17) with two homers and seven RBI in his last five games after enduring three injured list stints earlier in the year.
"I feel like it's different, I'm not your typical leadoff hitter," Voit said. "If you leave a mistake up, I can do some damage with it. It's just a different feeling, a different mindset because I got to set the tone for the guys.
"It's fun, I hope Boonie does it more. I just enjoy it."
Kyle Higashioka homered and started the four-run inning with an RBI double. Both hits scored Bronx native Andrew Velazquez, who had two hits and also stole a base - New York's 30th since the All-Star break.
"Really good production from those guys at the bottom to help us out big time tonight," Boone said.
Stanton added a homer in the eighth.
Jameson Taillon (8-4) took a shutout into the fifth before allowing four straight one-out hits. He allowed three runs and five hits in 5 1/3 innings for his seventh straight win.
Jake Cave homered and Jorge Polanco hit a two-run double off Taillon. Polanco also added a two-out RBI single off Zack Britton in the eighth and Miguel Sanó homered off Chad Green in the ninth.
"When you're down 4-0 and then 6-0, that is a challenge," Twins manager Rocco Baldelli said. "It's a real challenge, especially coming in here at Yankee Stadium playing a good team, but we battled back."
The Yankees are 19-5 since losing three of four in Boston July 22-25. Coming off a three-game sweep of the Red Sox, the Yankees remained one game ahead of Oakland for the AL's first wild-card spot.
"A lot of smiles," Velazquez said.
After the Yankees went up 6-0, Minnesota scored three in the sixth on Cave's homer and Polanco ground-rule double that just stayed fair. Taillon was lifted for Wandy Peralta and pounded his glove on the dugout bench.
Peralta got the final two outs of the sixth and pitched a perfect seventh. Britton struck out Josh Donaldson after allowing Polanco's hit and Green got his sixth save after allowing Sanó's 10th career homer in 20 games against the Yankees.
Gant allowed four runs and three hits in 3 1/3 innings.
Twins: OF Byron Buxton (fractured left hand) faced RHP Luke Farrell (strained right oblique) and saw about 25 pitches in live batting practice. Buxton will start a rehab assignment Friday in Triple-A St. Paul. ... Sanó and his wife had a baby girl Thursday morning and he is expected go on the paternity list this weekend before rejoining the team next week in Boston. A fifth staff member tested positive for COVID-19, Baldelli said. Earlier this week first base coach Tommy Watkins and hitting coach Edgar Varela tested positive. ... LHP Lewis Thorpe (strained left shoulder) was placed on the injured list and RHP Edgar García was optioned to Triple-A St. Paul. ... RHP Kyle Barraclough and LHP Andrew Albers had their contracts purchased from St Paul. Albers became the 31st pitcher used and allowed one run in four innings. "That was enormously impressive," Baldelli said.
Yankees: A second opinion on RHP Luis Severino's tight right shoulder did not show any structural damage. Severino will not throw the rest of this week and could join the Yankees on their upcoming West Coast trip to meet with doctors in person. "Overall, it was pretty good news from an MRI standpoint," Boone said. ... 3B Gio Urshela (strained left hamstring) could start a rehab assignment by early next week. ... SS Gleyber Torres (sprained left thumb) is expected to start taking swings in the next day or two. ... RHP Clay Holmes (COVID-19) will throw a bullpen session Friday and could be activated Saturday.
UP NEXT: Minnesota rookie LHP Charlie Barnes (0-2, 4.91 ERA) opposes New York LHP Nestor Cortes (1-1, 2.55) on Friday.
Higashioka extends Yanks' lead with 2-run dinger
Kyle Higashioka rips a two-run home run to left field in the Yankees' 7-5 win vs. the Twins.