Denard Span and Brendan Harris homered for Minnesota, which moved a half-game ahead of the White Sox. Chicago lost 14-3 at Kansas City.
Liriano missed all of last season after Tommy John surgery and went 0-3 with an 11.32 ERA in three starts before being sent down in April. He dominated at Triple-A Rochester, going 10-0 with a 2.67 ERA in his last 11 starts, and was openly frustrated as the Twins waited until Friday to call him up.
Minnesota is hoping Liriano's return will bolster its postseason push, and the left-hander did nothing to dampen those hopes Sunday. Liriano, who went 12-3 with a 2.16 ERA and 144 strikeouts before arm problems cut short his rookie year, allowed three hits, walked three and struck out five against the Indians.
Span went 2-for-4, and Nick Punto and Mike Lamb each had run-scoring triples for the Minnesota.
After breezing through two innings on 19 pitches, Liriano was tested in the third, facing a bases-loaded situation after two walks and a throwing error by shortstop Harris. Liriano threw 34 pitches in the inning but struck out Ben Francisco to end the threat.
Matt Ginter (1-3), making his fourth start of the season, allowed five runs and five hits in six innings for the Indians.
Cleveland cut the lead to 5-1 in the seventh when Jason Kubel misplayed Grady Sizemore's long flyball in left field, allowing Franklin Gutierrez to score from first.
Francisco hit his 11th homer in the eighth but Span went deep for his second of the season in the bottom half.
Notes: Twins manager Ron Gardenhire said OF Michael Cuddyer would report for his rehab assignment at Triple-A Rochester on Monday. Gardenhire said he thinks Cuddyer, out since June 30 with a strained tendon in his left index finger, will need about four or five games in Rochester before he's ready to return. ... Cleveland has homered in 25 of its last 29 games.