Thomas was especially busy in a frantic third period, during which he stopped all 19 Rangers shots and nailed down his 34th victory this season.
Patrice Bergeron scored the go-ahead goal in the second period and Dennis Seidenberg also tallied as the Bruins won for the fifth time in six games, securing both the division title and the second seed in the Eastern Conference.
It was also Boston's first triumph over the Rangers in four tries this season.
Marian Gaborik scored for conference-leading New York, which saw its four-game winning streak come to an end.
Henrik Lundqvist made 19 saves for the losers.