The Twins have won three of four and used the long ball in support of Kevin Correia (6-4), who won for just the second time in seven starts.
Dozier hit a three-run shot in the second inning to overcome Minnesota's early 1-0 deficit and Morneau contributed a two-run blast as part of the Twins- three-run sixth. The Twins built a 7-1 lead through six innings.
Correia lasted 6 2/3 innings, giving up two runs on five hits with six strikeouts. Glen Perkins picked up his 18th save with a perfect ninth, during which he had two strikeouts.
Chicago fell for the sixth time in seven games with the loss going to Chris Sale (5-6). He surrendered four runs on eight hits in five innings.