Tampa Bay entered the contest with just two wins in 17 tries against Boston this season and appeared to be heading for another defeat trailing, 4-1, heading into the seventh. But Jared Sandberg led off with a double and Abernathy singled him home to chase Red Sox starter Tim Wakefield.
Bobby Howry (3-5) entered and hit Felix Escalona before Damian Rolls sacrificed. A groundout by rookie Carl Crawford scored Abernathy before Winn connected to give the Devil Rays their first lead.
Devil Rays starter Victor Zambrano (8-8) allowed four runs and six hits in six innings. Lance Carter allowed a two-run homer to Nomar Garciaparra in the ninth but was effective over the final three innings and notched his second save.