Arvid Soderblom made 28 saves, and Alex Vlasic had two assists for the Blackhawks (14-17-6), who had lost eight of nine since Dec. 6.
Mikko Rantanen had a goal and two assists, and Wyatt Johnston had three assists for the Stars (25-7-7), who are 4-0-2 in their past six games. Jake Oettinger made 30 saves.
Ryan Donato and Nick Lardis scored in the shootout for Chicago. Soderblom allowed Matt Duchene to score, but made saves on Jason Robertson and Johnston with Rantanen losing the puck in the second round.
Bertuzzi put the Blackhawks up 1-0 on their first shot on goal at 3:20 of the first period, taking a cross-ice pass from Vlasic for a snap shot in the right face-off circle.
Nils Lundkvist tied it 1-1 at 11:31 with a one-timer from the point set up by Rantanen and past a screen from Sam Steel.
Jason Dickinson put the Blackhawks back in front 2-1 at 10:37 of the second period. He carried the puck through the neutral zone and beat Oettinger’s blocker with a wrist shot from between the circles.
Justin Hryckowian scored 55 seconds later at 11:32, chipping in a bouncing puck just after Johnston hit the left post with a snap shot.
Rantanen gave Dallas a 3-2 lead at 11:18 of the third period when he slid a rebound past a sprawling Soderblom off a shot from Johnston. He has 12 points (two goals, 10 assists) on a six-game streak.
Bertuzzi tied it 3-3 at 12:25, finishing near the net after a point shot from Vlasic deflected off Connor Murphy in the slot and rolled to him at the top of the crease.
Soderblom made saves on a pair of Stars breakaways in the third. Jamie Benn was denied by a left pad save at 11:26 and Rantanen had a snap shot turned away at 14:35.