Glen Murray, Mark Mowers, Milan Jurcina, Patrice Bergeron and Marc Savard also scored as the Bruins, who led 4-0 after two periods, improved to 4-0-1 in their last five games and 5-1-1 in their last seven.
Bergeron extended his point streak to 10 games. He has six goals and 11 assists during the span.
Boston's Tim Thomas stopped 37 shots. He lost a bid for his second shutout this season - and second in four games - when Chicago's James Wisniewski scored 1:35 into the third.
Bryan Smolinski and Denis Arkhipov also scored early in the third for the Blackhawks, 9-4-3 since Denis Savard took over as coach.
Chicago's Nikolai Khabibulin made his 10th straight start, but was pulled for the first time this season after allowing three goals on seven shots in the first period.
Brian Boucher replaced him to start the second, and surrendered one goal on 13 shots.
Boston jumped out to a 3-0 lead in the first on goals by Murray, Mowers and Jurcina.
Murray opened the scoring 5:51 in, tipping in P.J. Axelsson's shot at the edge of the crease.
Mowers' short-handed goal with 3:42 left in the first made it 2-0. From the low edge of the right circle, Mowers spun and surprised Khabibulin with a low shot.
Just over a minute later, Jurcina extended Boston's lead to 3-0, scoring on screened shot from the top of the right circle.
Bergeron's power-play goal with 4:53 left in the second made it 4-0. He knocked the puck in from the edge of the crease following a turnover by Jassen Cullimore.
The Blackhawks scored three times in a 4:19 span early in the third to cut it to 4-3. Wisniewski connected on a screened shot from the top of the right circle at 1:35 while the teams were skating 4-on-4 to make it 4-1.
Smolinksi was credited with cutting it to 4-2 45 seconds later when Lasse Kukkonen's shot struck him in the back, popped into the air and landed in the net.
Arkhipov trimmed it to 4-3 at 5:54 when he rammed in a rebound of Radim Vrbata's shot.
The Blackhawks had several prime chances later in the third, but missed the net or were stopped by Thomas. Thomas made a sprawling glove save on Chicago's Jeff Hamilton with 1:44 left.
Savard scored into an empty net with 11 seconds left to complete the scoring.
Notes: The Bruins and Blackhawks faced each other for the first time since Feb. 14, 2004. ... The crowd of 19,315 was Chicago's largest this season. ... Hamilton returned to the lineup after missing three games with the flu and a hip flexor injury. ... Blackhawks D Jim Vandermeer was a healthy scratch for the third straight game. ... Boston C Yan Stastny was a healthy scratch. ... Chicago F Peter Bondra, who scored his 500th NHL goal last week, took a hard hit to the upper body from Bruins D Brad Stuart just 27 seconds into the game. Bondra returned at the start of the second period.