Thomas yielded a goal to Simon Gagne just over 1 minute into the game but then shut the door, turning aside nine shots in the second period and 11 in the third, as the Bruins grabbed the series advantage.
Nathan Horton tied the score 4:24 into the middle frame, scoring on assists from Milan Lucic and David Krejci.
Then, 11 1/2 minutes later, Patrice Bergeron got control of the puck in the right circle and took his time looking for an opening, eventually finding Marchand streaking down the left side. The Bruins' center shook off a defender and one-timed the pass into the net past Lighting goalie Mike Smith for the tie-breaker.
Boston's Rich Peverley added an empty-netter with 13 seconds left.
Smith stopped 17-of-19 shots for the Bolts, who will attempt to knot the series again in Wednesday's Game 6 in Tampa.