Ott skated up the middle, split two defenders, and fired a wrist shot past Antti Niemi to make it 5-4 at 4:07 of the final period.
Loui Eriksson and Ott scored for the Stars in a 35-second span early in the second period.
Dallas' Mike Modano picked up his 549th goal, tying Ron Francis for 25th on the career list. Mike Ribeiro also scored and Brad Richards had two assists for the Stars, 7-1-2 in their last 10 at home.
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.
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.
Chicago made a strong early push with an 11-0 shots edge in the first five minutes, and 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 goal 35 seconds later that went in off a Chicago defenseman gave Dallas the lead.
Blackhawks coach Joel Quenneville then replaced Huet with Niemi after Huet had yielded four goals in 10 shots.
The Blackhawks tied it at 4 with 3.5 seconds left in the second when Kane knocked a rebound past Turco.
NOTES: The Blackhawks held a 21-8 shots advantage after one period. ... 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. ... Stars coach Marc 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 named to the Latvian Olympic team. ... The Stars won the first game with the Blackhawks this season, 4-3 in Chicago on Oct. 17.