Slowey (12-6) gave up two runs over five innings in his second start since being sidelined with a strained right triceps. The right-hander had not won since beating Oakland on Aug. 15, when he was lifted after seven no-hit innings.
The original Washington franchise moved to Minnesota after the 1960 season and became the Twins, which took two of three in the series. They have won eight of nine and are have baseball's best record since the All-Star break at 39-16. The AL Central leaders will open a three-game series in Chicago against the second-place White Sox on Tuesday.
Talbot left after only 14 pitches with shoulder inflammation. He walked leadoff batter Denard Span on five pitches. Manager Manny Acta and the Indians' training staff quickly went to the mound to check on the right-hander, who spent early August on the disabled list with a strained back.
Talbot won his previous start Sept. 4 for his first win in more than two months. The rookie opened the season 8-6, but went 0-5 in 10 starts after beating the Cincinnati Reds on June 27.
Luis Valbuena, whose first-inning error led to two unearned runs, hit a two-run double in the second to get Cleveland to 5-2. Both runs were unearned after an error by Twins shortstop Alexi Casilla, who fielded a ground ball hit by Jayson Nix and threw wildly past first base.
Cleveland loaded the bases with one out in the fifth, but Slowey struck out Shin-Soo Choo and got Travis Hafner on a groundout in which second baseman Hudson ranged behind the bag and made a strong off-balance throw to first for the out.
Masterson, moved to the bullpen after 28 starts, struck out six over seven innings — the longest relief outing for Cleveland since Jake Westbrook worked seven on April 19, 2004, against Detroit. Acta said Saturday the right-hander would likely work "about eight more innings this season," in an effort to avoid overuse. Masterson has now pitched a career-high 173 innings.
NOTES: D.J. Reyburn umpired at first base after Angel Campos had an emergency appendectomy Saturday night. Both are in their first year as major league umps. ... OF Michael Brantley had two singles, extending his hitting streak to an Indians season-high 13 games, the longest streak by a Cleveland rookie since Coco Crisp hit in 13 straight in 2003. ... Twins LHP Jose Mijares worked a scoreless eighth in his first outing since being sidelined by a right knee injury Aug. 12. ... Twins LHP Brian Fuentes pitched a perfect ninth. He had not worked since Aug. 28 due to a strained back.