The Bruins tied it on the power play when Andrew Ference kept the puck in at the blue line, and Rich Peverley finished it off with a wrist shot.
But it was in the second period that the teams really opened things up.
Toews tipped in Rozsival's shot to put the Blackhawks back in the lead with 6½ minutes gone. Just over two minutes later, Chicago took its first two-goal lead of the series when Kane converted a rebound to make it 3-1.
It stayed that way for six minutes before Milan Lucic deflected Chara's shot into Crawford and then put back his own rebound to make it a one-goal game. Forty-nine seconds later, Kruger stuck with the puck until he had poked it past Rask and into the net to make it 4-2.
That's when Boston got some luck.
Chara's shot from the center of the blue line deflected off Crawford's left shoulder and over the net, where it hit the back wall, bounced back onto the top of the net and landed in the slot, right in front of Bergeron. He chipped it in to make it 4-3, then tied it two minutes into the third.
"You think you have a good lead at 3-1 and they made it 3-2. Then we had 4-2 and they scored on the power play," Kane said. "It was back and forth the whole game but a fun game to play."
Patrick Sharp gave Chicago a 5-4 lead with 8:41 left in regulation — on an assist from Marian Hossa, who missed Game 3 with an undisclosed injury — but it lasted only 55 seconds before Boychuk tied it.
Notes: Bruins Hall of Famer Bobby Orr, who also played briefly for Chicago, was in the crowd, waving a yellow towel in support of the Bruins. ... Boston killed 29 consecutive penalties dating to Game 5 of the Eastern Conference semifinals, including the first 13 Chicago opportunities of the finals. ... The Blackhawks had the first seven shots of the game despite a penalty that left them short-handed. ... Jagr assisted on both goals by Bergeron, giving the 1999 NHL MVP 199 career postseason points. He is fifth all-time. ... Midway through the first, Boston's Shawn Thornton hit the scoreboard when he lofted the puck out of the zone.