Marcus Thames also hit a two-run homer for the Tigers, who completed a three-game sweep of the Twins for the first time since April 2002. Detroit outscored Minnesota 33-1 over the weekend.
"You can't forget Minnesota has been a great team for the last few years," Rogers said. "We might have caught them at a good time."
It also gave Detroit 16 wins in April, the most since 1993, which was the last year it finished over .500. The Tigers also finished April with five shutouts.
The Twins have lost eight of their past 10. The last time they scored one run in a three-game series was June 5-7, 1981, in Detroit, according to the Elias Sports Bureau.
"It was a disappointing series," Minnesota manager Ron Gardenhire said. "They just killed us."
Rogers (4-2) walked one and struck out four. He is 7-3 against Minnesota since 1998.
"He led us with his fastball and kept us off balance with his changeup," Twins designated hitter Rondell White said. "He did what he had to do."
Rogers' only trouble came in the second when Joe Mauer walked to lead off the inning and Torii Hunter followed with a single. But Rogers rebounded to strike out Justin Morneau and second baseman Placido Polanco made a nice play on White's grounder to get the forceout at second.
He dove behind the base and flipped a blind throw over his shoulder to shortstop Carlos Guillen.
"I saw the bag, I knew he (Guillen) was there somewhere," Polanco said. "At the same time, I didn't want to throw the ball too hard."
"Vintage pitching and defense today," Tigers manager Jim Leyland said.
Kyle Lohse (1-2) got the loss for Minnesota, allowing six runs and eight hits in 5 2/3 innings. He walked two, struck out one and hit three batters.
"I threw like I needed to throw. I didn't think I made any bad pitches," Lohse said. "One good hit for a homer and a couple of hit batters and you look up and you're six runs down."
After a leadoff single by Craig Monroe in the fifth, Thames hit Lohse's first pitch out to left-center for his fourth homer of the season.
The Tigers put it away with four runs in the seventh on Wilson's bases-loaded double and Polanco's RBI single.
- Minnesota placed designated hitter Ruben Sierra on the 15-day disabled list with a strained left biceps. To replace Sierra on the roster, Minnesota recalled left-hander Dennys Reyes from Triple-A Rochester.
- Monroe went 2-for-4 to stretch his hitting streak to five games (9-for-20).