Tomlin (5-5) has won back-to-back starts for the first time this season. He did not walk a batter and the only run he allowed came in on a groundout by Jose Molina in the fifth after Will Rhymes had tripled.
Vinnie Pestano and Chris Perez each gave up a hit in tone inning of work, with Perez picking up his 24th save. It was Cleveland's third win in a row.
Jeremy Hellickson (4-5) lost his fifth consecutive decision, allowing two runs on five hits in six frames.
Tampa Bay first baseman Luke Scott established a franchise record by extending his hitless streak to 39 at-bats. He went 0-for-3.