Lackey (2-4) broke personal a three-start losing streak with the efficient performance, which he was able to complete before a three-hour rain delay halted the game in the seventh inning.
The right-hander surrendered one unearned run, didn't issue a walk and struck out five in the victory.
Dustin Pedroia drove in three runs, including a two-run homer after the delay, and Will Middlebrooks also went deep as the Bosox reeled off their fifth straight win overall.
Twins starter Pedro Hernandez (2-1) allowed three runs on nine hits over 4 1/3 innings.
Trevor Plouffe had two hits for Minnesota, which dropped a fifth straight home game.
Celebrity Families of 2014 [PHOTOS]