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.
Beyonce flaunts bikini body, Blue Ivy in vacation pics
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need