Gonzalez delivered a run-scoring single in the third inning, staking the Red Sox to a 2-0 lead, then cracked a two-run shot in the fifth to double the advantage.
Carl Crawford finished 3-for-5, knocking in a first-inning run for the Bosox, who snapped a four-game skid.
Boston starter Franklin Morales (3-2) held the Twins to one run on three hits over six innings.
Twins starter Nick Blackburn (4-7) was touched for four runs on nine hits in a five-inning effort.
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