After playing four extra periods in the first two games, the Bruins made an early night of it with second-period goals by Daniel Paille and Patrice Bergeron to win 2-0 and take a 2-1 lead in the Stanley Cup finals.
Rask stopped 28 shots for his third shutout of the 2013 playoffs.
Corey Crawford made 33 saves for the Blackhawks.
Game 4 is Wednesday night in Boston before the matchup of Original Six teams returns to Chicago for a fifth game. The teams split the first two games there, with the Blackhawks winning Game 1 in triple-overtime and the Bruins stealing home-ice advantage on Paille's goal in the first OT of the second game.
But this time the intrigue came before the opening faceoff instead of after the end of regulation.
Bruins defenseman Zdeno Chara and Chicago forward Marian Hossa were both injured during warmups. But while Chara needed just some stitches after his collision with teammate Milan Lucic, Hossa was a late scratch with an unspecified injury.
Hossa, who has three game-winning goals in the playoffs this year, was tied for the team lead with 15 playoff points and was third on the Blackhawks with 17 goals during the regular season.
It was a loss the Blackhawks couldn't afford.
Not with Rask stopping everything that came his way.
The Bruins' goalie, who was a backup to Conn Smythe-winner Tim Thomas in the team's 2011 Stanley Cup run, didn't face as difficult a test as in the first period of Game 2, when the Blackhawks sent 19 shots at him but managed just one goal. But he stymied them all game and got some help from the post on Bryan Bickell's shot with 42 seconds left in the game.
The puck caromed off the right post and the goal light flickered on briefly, but play continued for another 30 seconds before the whistle blew and the game degenerated into fisticuffs. Chara was on top of Viktor Stalberg, pounding away, and Andrew Shaw got the better of Brad Marchand.
By the time it was all sorted out, the benches were a little emptier but the scoring column for Chicago was still blank.
After a scoreless first period, the Bruins made it 1-0 when Paille slapped in the puck at 2:13 of the second, falling to one knee for extra power. It stayed that way until late in the second, when the Bruins picked up their first power plays of the game on two nearly identical plays, with a Bruin racing to the net and a Blackhawk undercutting his skates and sending him crashing into the left post.
Boston set up their offense during the 11-second two-man advantage, and just five seconds after it expired — but before Dave Bolland was able to get back into the play — Jaromir Jagr slid one across the middle, past Lucic in the center to Bergeron on the other side for the easy one-timer.
It was Jagr's 197th career playoff point in 199 games, moving him into sole possession of fifth place on the NHL's all-time postseason points list.
Notes: Jagr had been tied with Paul Coffey on the career postseason scoring list. ... Two of Jagr's playoff points came on goals scored against the Blackhawks when they were swept by Penguins in 1992 final. ... Boston's Gregory Campbell, who broke his leg blocking a shot in Game 3 of the Eastern Conference finals, attended the game. ... The Bruins have killed off 27 straight penalties in the playoffs. ... Boston's David Krejci entered the game tied with Chicago's Andrew Sharp for the most goals in the postseason with nine. The Bruins center entered the game leading all scorers with 23 points. ... The Bruins are attempting to win a Cup for the second time in three seasons for the third time in their history. They also did it in 1939 and '41 and again in 1970 and '72. ... Bruins won their seventh straight home playoff game. ... The Blackhawks fell to 3-5 on the road in the postseason. ... Ben Smith, who played just one game this regular season and none in the playoffs, replaced Hossa in the lineup. ... Stalberg replaced Brandon Bollig in the lineup for Chicago.