Ryan Greene put the Blackhawks ahead 3-2 at 9:38 of the third, finishing a 3-on-1 by beating DiPietro short side.
Bedard scored less than three minutes later at 12:20 to put Chicago up 4-2.
Frondell's power-play goal gave Chicago a 1-0 lead at 6:04 of the first period, a one-timer from the right circle that beat DiPietro high glove.
"I thought 'Frondy' played great," Blackhawks coach Jeff Blashill said. "I thought he played a great game. It was unfortunate not to get the win out of it based on when guys play as good as they play. But again, that's the way it goes."
Pastrnak tied it 1-1 at 13:05 after Pavel Zacha sent him on a breakaway with a backhand stretch pass and he chipped the puck over Soderblom's glove.
"It was amazing," Pastrnak said of the pass. "It was a heck of a play by Pavel, and for me, it's an easy job after he makes a play like that."
Pastrnak, who was named Bruins captain September 27, trails only Johnny Bucyk (545) and Phil Esposito (459) in goals in team history.
"That's a huge milestone," Bruins coach Marco Sturm said. "Doing that with one franchise, especially a franchise like the Boston Bruins is pretty amazing. It just shows you what kind of player he is, and what kind of a goal scorer he is. It's pretty amazing and he's still not done yet. That's the nice part of being 30-years-old, there's still more to come."
Frondell's second goal of the game gave Chicago a 2-1 lead at 3:31 of the second period when he redirected Tyler Bertuzzi's shot from the left circle over Soderblom's shoulder.
Casey Mittelstadt tied it 2-2 at 12:34. James Hagens stole the puck with a stick check just inside the offensive blue line and fed Mittelstadt, who sent a wrist shot past Soderblom from the slot.
"Heck of a way to get two points for us," Pastrnak said. "Sometimes this is the kind of game it takes to get back in the winning column. It wasn't easy when you get a couple of losses, you want to get that win. It was a great job by the whole group to stick with it. It wasn't pretty, but at the end of the day, it's two points and that's all we were focusing on."
NOTES: Blackhawks forward Patrick Kane got his 900th NHL assist on Frondell's first goal. He became the 21st player in NHL history, and first U.S.-born player, to reach the milestone. Kane trails only Sidney Crosby of the Pittsburgh Penguins (1,111) in assists among active players. …Frondell became the seventh Sweden-born teenager in NHL history with multiple multi-goal games in his career. He joined Lucas Raymond (three times), Elias Pettersson (three), Leo Carlsson (two), Elias Lindholm (two), Gabriel Landeskog (two) and Mats Sundin (two). …The Bruins won their fifth straight home game and improved to 6-1-0 on home ice.