It was the first shutout for Lowe (6-1) since August 2005 and the fourth of his 16-season career. He walked four and didn't strike out a batter.
With Lowe's sinker working, 22 of the 27 Twins outs were the result of ground balls. The Indians turned four double plays behind Lowe.
Twins shortstop Brian Dozier had half of the team's hits Tuesday.
Minnesota starter Jason Marquis (2-3) was touched for nine hits and five runs in five innings. The Indians had three home runs in a four-hitter span off Marquis in the fifth.
Shin-Soo Chin led off the fifth with his second home run of the season and, after a strike out, Cabrera connected for his fourth. Four pitches later Santana hit his fifth of the season for the 5-0 lead.