Liriano (1-5), recently reinstated to the Twins' rotation after an ineffective start to the season, earned his first win, silencing the Athletics on three hits.
The left-hander struck out nine and issued a pair of walks for last-place Minnesota, which logged its first three-game sweep of the season.
Relievers Alex Burnett and Jeff Grey completed the shutout with a scoreless frame each.
Josh Willingham smacked his second homer in two games, launching a two-run shot in the fifth to finish with three RBI for the Twins.
A's starter Tyson Ross (2-6) dropped his third consecutive game, allowing four runs on six hits over five full innings.