Milan Lucic had two goals and an assist for the Bruins, who had won five straight and nine of 10. Patrice Bergeron scored a power-play goal and David Krejci finished with two assists.
"Not disappointed in our effort," Bruins coach Claude Julien said. "There's certain things you're going to want to fix for next game. But as far as the game is concerned, it was a hard-fought game."
Rask made an astounding 59 saves in a finals marathon that passed Pittsburgh's 4-3 win over Detroit on June 2, 2008, when Petr Sykora scored at 9:57 of the third overtime.
Game 2 is Saturday night at the United Center.
"That's playoff hockey," Bruins center Rich Peverley said. "It's fun to watch, so we'll think about this until we get out of here and then shake it off and get ready for Saturday."
The Blackhawks won for the eighth time in nine games and improved to 10-1 at home in the playoffs.
Bolland and Johnny Oduya scored in the third period for Chicago, which never would have made it to the third overtime if not for an impressive performance by goaltender Corey Crawford. Brandon Saad had his first goal of the playoffs.
Crawford gave the Blackhawks a chance by standing his ground when the Bruins had repeated opportunities in the extra sessions.
Shawn Thornton and Daniel Paille skated in for a 2-on-1 in the first OT, and Crawford turned away Thornton on the doorstep. He denied Peverley and Tyler Seguin in rapid succession, and helped Chicago kill off two power plays when it was whistled twice for too many men on the ice.
Nathan Horton hit the post in the first extra session, and Zdeno Chara's slap shot deflected off Jaromir Jagr and then the inside of the right post at the very end of the second overtime.