Liriano (2-7) notched his first victory in nearly a month, holding the White Sox to one run on four hits and a pair of walks.
The left-hander struck out five for the Twins, who claimed the opener of a three-game series.
Mauer's sacrifice fly in the first inning put Minnesota ahead for good, while Ben Revere added four hits for the Twins.
Chicago starter Jake Peavy (6-4) was touched for three runs on 10 hits over six innings.
Alexei Ramirez went 2-for-3 with an RBI for the American League Central-leading White Sox.
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