The Red Sox won their third straight while the Twins have lost three in a row.
Pedroia singled to open the 10th against Josh Roenicke (1-1) and went to second when David Ortiz drew a walk. A sacrifice by Will Middlebrooks moved the runners up and Stephen Drew was walked intentionally to load the bases.
Gomes came through with a fly ball to center.
That run gave Alex Wilson (1-0) his first major league victory after he recorded the final out of the ninth. Koji Uehara turned in a perfect bottom of the 10th for his first save.
A two-run homer by Pedro Florimon gave Minnesota a one-run lead in the third, but Boston tied it in the seventh on an RBI single from Jacoby Ellsbury.