Liriano (1-3), making his first start since he was recalled from Triple-A Rochester, gave the Indians just three hits and struck out five over six innings.
The Twins went ahead on Harris' solo home run to left in the third inning and never trailed. Span's homer, also a solo shot, completed the scoring in the eighth.
A solo homer by Ben Francisco and RBI double by Grady Sizemore provided the Indians' runs.
Matt Ginter (1-3) was the loser, allowing five runs and five hits in six innings.