Less than 2 minutes into the overtime, the Bruins' Andrew Ference was whistled for a 5-minute major penalty and a game misconduct for slamming New York's Ryan McDonagh into the boards while the defenseman was in a vulnerable position.
That gave the Rangers a long, 4-on-3 power play. After missing on some tries, Gaborik found the net when Boston's Tuukka Rask couldn't make a third sprawling save during a flurry in front of the net.
Gaborik and Ryan Callahan also scored in the second period and Henrik Lundqvist turned aside 32-of-34 shots for the Rangers, who lengthened their lead over the Bruins atop the Eastern Conference to three points.
Ference and Adam McQuaid scored for the Bruins, who lost for just the third time in 18 home games.
Rask finished with 30 stops for Boston.