Kevyn Adams scored the tying goal late in regulation, Aaron Johnson had a power-play goal, and Kris Versteeg scored short-handed for Chicago (4-1-1).
Brad Richards had a goal and an assist, and rookies James Neal and Fabian Brunnstrom also scored for the Stars (1-4-1).
With the game even at 2, Neal's one-timer from just outside the slot put Dallas in front at 14:51 of the second period.
But the Blackhawks tied it at 3 with 1:36 left in regulation on Adams' goal from the high slot.
Johnson opened the scoring with a power-play goal at 6:42 of the first period.
Richards tied it at 1 with 45 seconds gone in the second when his centering pass glanced off Chicago defenseman Brent Sopel and off Niemi's pads while Dallas was on a power play.
Richards set up Brunnstrom for a power-play goal at 8:04 of the second period to give Dallas a 2-1 lead.
Versteeg's goal on the penalty-kill at 12:10 of the second period tied it at 2.
A total of 141 penalty minutes were assessed in a game that included five fights, three misconducts and a match penalty.