Bauer (1-2) pitched 6 1/3 innings and struck out seven batters while allowing two runs on three hits and two walks. Abraham Almonte had two hits for Cleveland, which swept Minnesota in the three games of the series after Wednesday's game was postponed.
Boone Logan, Bryan Shaw, Andrew Miller and Cody Allen combined for 2 2/3 innings of relief, allowing just one hit.
The Indians (8-7) had lost seven of their previous nine games heading into the series.
Twins starter Ervin Santana went six innings before being relieved by Tyler Duffey (0-1) to start the seventh.
Duffey allowed two hits in one-third of an inning and both runners scored as the Twins used three relievers to get through the seventh inning. Santana doubled off Taylor Rogers for the first run of the inning. Rogers and Matt Belisle each walked home a run with the bases loaded.
Minnesota wasted another strong start from Santana, who stretched his scoreless inning streak to 22 innings before Santana doubled home Almonte in the fifth. Santana gave up four hits and three walks in six innings, and struck out five batters. The right-hander has a 0.64 ERA through four starts.
Max Kepler had two hits and scored a run for the Twins, who scored both their runs in the fourth against Bauer. Joe Mauer doubled to start the inning and later scored on a bases-loaded balk by Bauer. Kepler scored on Jorge Polanco's sacrifice fly.
Bauer had allowed 10 runs in 10 2/3 innings in his first two starts of the season. But he was in control against Minnesota. Mauer's double was the first hit allowed by Bauer and he retired nine of the final 10 batters he faced.
After their 6-3 start to the season, the Twins returned home and have lost five of their past six games. Molitor was ejected for the first time this season and fifth time in his managerial career after catcher Jason Castro struck out in the eighth on a check swing that was ruled a swing by home plate umpire Alan Porter.
NOTES: Cleveland manager Terry Francona said "everything points" to 2B Jason Kipnis (shoulder) returning to the lineup during the weekend in Chicago. Kipnis took Thursday off after playing in rehab games this week. ... Minnesota used the same lineup and batting order for the second straight game, the first time this season manager Paul Molitor has penciled in the same look in more than one game. ... Twins 1B Joe Mauer had a double to lead off the fourth inning for his first extra-base hit of the season. ... Molitor said there has been no thought to sending CF Byron Buxton to Triple-A Rochester. Buxton was 0-for-2 with a strikeout on Thursday and is hitting .082 this season with 24 strikeouts in 49 at-bats. ... Cleveland will start RHP Corey Kluber (1-1, 6.38 ERA) on Friday against the White Sox. Minnesota hosts Detroit and will have LHP Hector Santiago (1-1, 1.47) on the mound.