Chicago (24-37-11) has lost seven in a row (0-5-2). Kevin Lankinen allowed five goals on 20 shots before being replaced at the start of the third period by Collin Delia, who made nine saves.
"Overall, I thought we competed much better," Blackhawks coach Derek King said. "Happy with the way we competed. We had some chances, we just couldn't score. I'm sure we could have used a couple of stops here and there. I'm sure the goalies feel the same way. I'll never throw goalies or anything (under the bus). We need to be better in front of them, I guess, and clean up some of the mess.
"We needed something to change, so that's why I changed (goalies). A little shaky, that's all."
Benn gave the Stars a 1-0 lead at 4:14 of the first period, converting on a rebound in front one second before a power play expired.
Philipp Kurashev tied it 1-1 at 8:09. After John Klingberg couldn't handle a pass in the neutral zone, Kurashev skated in on a 2-on-1 and scored when his pass redirected in off Esa Lindell.
Jonathan Toews gave Chicago a 2-1 lead with a power-play goal at 11:24. He flipped the puck toward the net from the left-wing boards, where it was again redirected in by the stick of Lindell.
Pavelski tied it 2-2 with a redirection on the power play at 13:45. He then intercepted a pass by Kirby Dach and fed Hintz, who scored from the high slot to make it 3-2 at 1:47 of the second period.
"[Dach] had that turnover inside our blue line," King said. "I looked at it. You could see what he was trying to do, hit the weak-side 'D' jumping up. They knocked it down. Those are the kind of mistakes that are kind of haunting us of late."
Boris Katchouk tied it 3-3 at 9:11 with a one-timer off a cross-ice pass from Erik Gustafsson.
Robertson put Dallas back in front 4-3 at 11:13, banking a shot off Lankinen from below the goal line, and extended the lead to 5-3 at 14:32 with a shot from the top of the right circle.