Fister -- who had a 2-0 lead before he threw his first pitch -- tossed five no-hit innings before giving up a solo shot to left by Brian Dozier leading off the sixth. The right-hander ended his day allowing two runs on two hits over 7 2/3 innings. Fister walked one and struck out seven, throwing 110 pitches.
"He was terrific," manager Jim Leyland said. "He did a great job of making them miss the ball."
"My mindset is just to go out there and get as many outs as possible," Fister said. "Trying to get deep in the game is the No. 1 thing, and I do that by getting bat contact early on."
Fister said it was the defense that was really working for him, rather than any particular pitch.
"They hit a lot of balls hard," Fister said. "Luckily for me it was right at guys. It says a lot for the defense today and that's why we have them."
The Tigers wasted no time getting runs on the board. Hitting second in the order, Hunter hit his 300th career home run in the first inning -- a two-run shot to left field that scored Austin Jackson, who led off the game with a single.
"It's special," Hunter said. "Just hitting my first home run in old Tigers Stadium against the Tigers with the Twins, to hit 300 against the Twins in the Tigers uniform at Target Field -- it's special. It's kind of weird, but it's special. I'm glad I got that monkey off my back."
Three innings later, Jackson slammed a two-run homer of his own to the second deck in left. The homer also scored Alex Avila, who reached a batter earlier with a two-out single -- his second hit of the game and his first hits since June 6.
"This guy, he's special," Hunter said of Jackson. "He's the table-setter. He gets it done. Just having him back on top of the lineup, getting on base, going first to third, stealing bases, playing great defense, good at-bats, it's great to have Austin back and I'm telling you, he's the sparkplug we need."
Twins starter P.J. Walters lasted only 5 1/3 innings, allowing four runs on nine hits with three walks and four strikeouts.
"Right out of the gate, the two-run homer put us in a hole and didn't get much better from there," Walters said. "My location was terrible all day long. The two homers are what ended up biting us, but the location wasn't good even on the guys I got out."
Minnesota did little offensively to help Walters, not getting its first baserunner until the fourth, when Fister gave up a two-out walk to Ryan Doumit. Two innings later, Fister gave up the Dozier home run. Dozier would later double off Fister for the Twins' second hit.
After Dozier's double in the eighth, Fister walked Pedro Florimon. Right-hander Joaquin Benoit replaced Fister and got out of the eighth, but not before giving up a base hit to Clete Thomas which brought Dozier in from second to make it 4-2.
"You have to find a way to get hits and score runs," Twins manager Ron Gardenhire said. "It was the third game out of the last four we had just three hits and that's not going to get it done. We thought maybe [Saturday] night would carry over, but it didn't."
After Hunter made it 5-2 with an RBI double in the ninth, Benoit got the final three outs for his fourth save, with Leyland opting not to use closer Jose Valverde.
"That was a huge hit [by Hunter] because it changes the whole complexion of the game," Leyland said. "So we're doing OK. Benny did a great job closing it out. I just felt his repertoire was a little better for the type of hitters [the Twins] had hitting, so I decided to stay with him today."
Kelly Erickson is an associate reporter for MLB.com.