But Boston quickly responded against Joel Peralta in the next half-inning when Daniel Nava drew a lead-off walk and Gomes followed by socking the first pitch he saw inside the left-field foul pole for a walk-off game-winner.
Nava also went deep for the American League East-leading Red Sox, who took Tuesday's first game 5-1.
Bosox starter Felix Doubront settled for a no-decision after blanking the Rays on three hits over eight scoreless innings. He didn't allow a walk and struck out six.
Tampa Bay's Jake Odorizzi also pitched well, yielding one run on five hits over 5 2/3 frames.
Celebrity Families of 2014 [PHOTOS]