Dempster (2-3), who pitched five perfect innings to begin his previous start Tuesday, stumped Minnesota on four hits this time out.
The right-hander yielded only one walk and struck out six en route to lowering his ERA to 2.31 for the Cubs, who salvaged one victory in a three-game interleague series at Target Field.
Francisco Liriano (1-7) dropped his second straight start since returning to Minnesota's rotation, surrendering four runs on four hits in a 5 2/3-inning effort. He walked three.
Jamey Carroll went 2-for-4 with an RBI for the Twins.