The Twins took an 11-6 lead through just two innings and held on to win for the third time in four games.
Minnesota's attack was highlighted by a seven-run second in which Pedro Florimon drove hit a solo homer in his first trip to the plate and added a two-run double in his second appearance.
Aaron Hicks also had a two-run double in the second. Doumit contributed a two-run homer during a four-run first and Joe Mauer had two doubles and scored three times for the Twins.
Ryan Pressly (1-0) threw four scoreless innings of relief for the first victory of his career.
Allen Webster (0-1) was given the Boston start in place of Felix Doubront, who has been moved to the Boston bullpen. Webster was torched for eight runs on six hits in 1 2/3 innings.