Rask notched his third shutout of the post-season and second straight at home for Boston, which racked up a seventh straight playoff win at TD Garden.
The Finnish goalie made eight of his saves during the second period as Boston was notching a pair of goals to grab control of the contest.
Daniel Paille made it 1-0 two minutes into the middle frame when he stripped the puck from Dave Bolland deep in the Chicago zone and fired a turnaround wrist shot that beat Blackhawks netminder Corey Crawford to the short side.
Crawford finished with 33 saves for the Blackhawks, who will try to even the series in Wednesday's Game 4 at Boston.
Celebrity Families of 2014 [PHOTOS]