Thomas -- who spent the first eight years of his career with the Bruins -- was facing his former team for the first time. He won the Conn Smythe Trophy in 2011 while helping Boston win the Stanley Cup.
Boston won for the fourth time in its first six games after letting a two-goal lead slip away.
First-period goals by Daniel Paille and Dougie Hamilton put Boston in front, but Tampa Bay came back to tie it on a goal in the second period by Kris Versteeg and another in the third from Jesse Winchester.
Tuukka Rask stopped 27 shots to collect the victory. Thomas saved 37-of-40 shots.