Jackson's two-run blast came after Victor Martinez and Omar Infante had launched back-to-back solo shots earlier in the fourth for American League Central-leading Detroit, which secured at least a wild-card berth with the win.
Doug Fister (14-9) allowed two runs on eight hits over 6 1/3 innings to get the win, walking one and striking out seven.
Drew Smyly, Al Aburquerque and Bruce Rondon combined for 1 2/3 scoreless relief innings and Joaquin Benoit struck out the side in the ninth for his 23rd save.
Twins starter Scott Diamond (6-12) was tagged for four runs on nine hits in a 6 1/3-inning stint.
Chris Parmalee went 3-for-4 with an RBI and Ryan Doumit clubbed a solo homer for Minnesota.