Viciedo went 3-for-5 and Alejandro De Aza scored twice in Chicago's second consecutive win after losing six in a row.
Quintana (8-6) plugged along for six innings, allowing one run on eight hits and striking out five. Addison Reed picked up the save.
Mike Pelfrey (5-13) struck out six for the Twins, who have dropped six of their last seven. Pelfrey was rattled for three runs on nine hits in 4 1/3 innings.
Trevor Plouffe drove in two runs for the Twins and Brian Dozier collected three hits.