Slowey (10-2) gave up only three hits and struck out six. Going into Friday's games, Toronto's Roy Halladay had been the only pitcher in the majors with 10 victories. Chad Billingsley of the Los Angeles Dodgers was going for his 10th win Friday.
Joe Nathan recorded the last four outs for his 16th save.
Delmon Young had two doubles and two RBI for the Twins. He also robbed Lance Berkman of a home run in the ninth with a leaping catch.
In addition, Young scored on a squeeze bunt by Nick Punto in the fifth.
Minnesota won for the fifth time in seven games.
Roy Oswalt (3-4) suffered the loss in an eight-inning stint, his longest start of the season so far. He allowed five runs on 10 hits.