Brent Seabrook's goal 9:51 into OT ended a wild Wednesday night of offence and short-lived leads, sending the Blackhawks back to Chicago for Game 5 on Saturday all even instead of trailing 3-1.
It was a decided turnaround for Chicago after a listless performance Monday in a 2-0 loss that put the Bruins up 2-1 in the series.
The Blackhawks had six shots on goalie Tuukka Rask before the Bruins had any. Chicago also outhit the Bruins early and pounced on loose pucks when Rask left himself vulnerable by failing to control rebounds.
Rask had allowed just seven goals in seven games before the Blackhawks beat him six times on Wednesday. Although the Bruins rallied to tie it three times, the Blackhawks never trailed.