Chicago's Patrick Kane scored twice, giving him seven goals in his last five games. Troy Brouwer and Colin Fraser also had goals for the Blackhawks, who've lost both meetings with the Stars after sweeping four games from Dallas last season.
"We stuck with it and scored some opportunistic goals," Richards said. "It was a big challenge. They're probably the best team in the league, the way they move the puck and the talent they have. It's a big win."
The Blackhawks nearly tied it at 5 with 5:07 left but Marty Turco made two stops on point-blank attempts by Chicago captain Jonathan Toews.
"We had plenty of chances," Toews said. "We were sharp, we just weren't as diligent defensively as we normally are."
Turco stopped all 11 shots he faced in the final period with the help of five blocked shots by teammates.
"They played with their bodies on the line," Stars coach Marc Crawford said. "It was their determination and desire to win. It was a great job by a lot of players. There weren't any passengers tonight."
Chicago started the night as one of the league's hottest teams, having gone 7-1 in their previous eight games, and the Blackhawks made a strong early push with an 11-0 shots edge in the first five minutes.
The Blackhawks capitalized on the game's first power play when Brouwer fired a rebound past Turco at 3:10 of the opening period.
Dallas made it 1-all on its first shot of the game when Modano's power-play wrister from low in the left circle went in over Cristobal Huet's left shoulder at 5:14 in the first.
The Blackhawks went in front 3-2 on Fraser's first goal of the season late in the first, set up by a centering pass from Kris Versteeg.
Dallas tied it at 3 when Eriksson's shot dribbled through Huet's pads and over the goal line 57 seconds into the second.
Ott's fluky goal 35 seconds later that pinballed off the skate of a Chicago defenseman gave Dallas the lead.
"You laugh about it, but at the end of the day, they all count," Ott said.
Blackhawks coach Joel Quenneville then replaced Huet with Niemi after Huet had yielded four goals in 10 shots.
"I had to do something," Quenneville said. "They were going in too easy. It was an easy call."
The Blackhawks tied it at 4 with 3.5 seconds left in the second when Kane knocked a rebound past Turco.
Chicago held a 21-8 shots edge after one period with the help of three power plays, and the Blackhawks capitalized on two man-advantage situations.
"They had most of those shots on the power play," Ott said. "We're going to kill ourselves if we don't stay out of that box. From then on, every guy played hard but stayed within the rules."
Turco missed the two previous games with the flu. ... Chicago had killed 25 straight power plays before Modano's goal. ... D Trevor Daley (shoulder) returned to the Dallas lineup after missing five games. ... Crawford broke up his top line of Richards, James Neal and Eriksson. Neal was dropped to the second line and Jere Lehtinen joined the No. 1 trio on the right side. ... Versteeg and D Niklas Hjalmarsson rejoined the Blackhawks after missing a home-and-home weekend set against Nashville with flulike symptoms. ... Earlier Tuesday, Stars D Karlis Skrastins was picked for the Latvian Olympic team.