Tim Thomas out-dueled Nikolai Khabibulin in a tremendous goaltending battle, making 31 saves in regulation and overtime. Thomas also stopped Blake Wheeler in the first round of the shootout and Dave Bolland in the third round.
Axelsson then got one past Khabibulin, who had turned back 38 of 39 shots going into the shootout.
The Bruins won their fourth straight game and, along with Buffalo, leaped past Montreal into a share of first place in the Northeast Division. Chicago had a four-game winning streak snapped. The Blackhawks had been trying for their longest victory streak in almost six years.
Marco Strum gave Boston the lead with 54 seconds left in the second period and Chicago tied it midway through the third on a goal from Jonathan Toews. Both the regulation goals came on the power play.