Bruins goalie Tim Thomas came out of the crease to challenge Sauer at the left of the net on the decisive play, but the Rangers defensemen put a shot between Thomas' legs and into the goal, giving New York its first lead on its fourth unanswered goal.
Vinny Prospal began the comeback with a pair of second-period goals, pulling New York within 3-2, and Brandon Dubinsky netted the equalizer only 49 seconds before Sauer's game-winner.
The win enabled New York to solidify its hold on an Eastern Conference playoff spot with two games remaining.
Henrik Lundqvist turned aside 27-of-30 shots and Derek Stepan added an empty-net goal for the Rangers.
Daniel Paille, Nathan Horton and Chris Kelly each scored to help build the Bruins' 3-0 lead.
Thomas ended with 21 saves for Boston.
Celebrity Families of 2014 [PHOTOS]