Ortiz put Boston ahead to stay with a three-run shot in the first inning, added an RBI single in the third and connected for a two-run blast in the seventh as the Red Sox notched a fourth straight win.
Daniel Nava went 2-for-4 with a two-run clout and a sacrifice fly and Ryan Lavarnway also knocked in a pair for the Bosox, who pounded out 14 hits in the victory.
Craig Breslow (1-0) earned the decision with 1 2/3 innings of scoreless relief.
Twins starter Scott Diamond (3-4) was tagged for six runs on eight hits in a 4 1/3-inning effort.
Notable deaths of 2014 [PHOTOS]