Hicks belted solo shots in the fourth and sixth innings and also robbed Chicago's Adam Dunn of a homer with a sparkling grab in center field for the Twins, who notched their fifth win in seven games.
Morneau contributed a bases-clearing double and Trevor Plouffe added two RBI as Minnesota took the opener of a three-game series.
Pedro Hernandez (2-0) overcame a rocky start to go 5 1/3 innings for the victory, yielding three runs on six hits. The former White Sox prospect struck out four.
Chisox starter Hector Santiago (1-2) was roughed up for six runs (three earned) on eight hits in a 5 2/3-inning effort.