With the game even 2-2 and the teams 4-on-4, Modano skated to the net along the right side and beat Blackhawks goalie Nikolai Khabibulin after a centring pass from Philippe Boucher for Modano's 22nd goal of the season.
Dallas went 12-2-2 in its last 16 games to finish with 107 points and wrap up the sixth Western Conference playoff seed.
The Stars and San Jose Sharks have the same point total but the Sharks have one more victory to earn the fifth seed in the Western Conference.
Dallas will meet the No. 3 seed, the Northwest Division champion Vancouver Canucks, in the first round of the playoffs.
Chicago, which missed the playoffs for the eighth time in the last nine seasons, finished with 71 points, tied with Edmonton for second-fewest in the conference.
Bryan Bickell gave the Blackhawks a 2-1 lead at 12:27 of the third period with a one-timer from the high slot for Bickell's second goal of the season.
But Sergei Zubov got the tying goal for Dallas at 13:36 of the third, notching his 12th of the season on a shot from the point.
Brenden Morrow broke up a scoreless game with his 16th goal at 5:55 of the third period while the Stars were on a power play.
Jason Willliams' deflection for his 15th goal of the season 1:01 later pulled the Blackhawks even 1-1.
The Stars held a 22-18 shots edge through two periods and had the better scoring chances, but Khabibulin made several difficult stops to keep the game scoreless.
Notes: The Stars were without RW Jere Lehtinen (lower-body strain), C Eric Lindros (groin) and RW Matthew Barnaby (concussion). ... D Trevor Daley returned for Dallas after missing the previous three games due to an upper-body strain. ... The Stars reached 50 wins for the third time since 1998-99. The Detroit Red Wings are the only other NHL team win three 50-win seasons during that span. ...Out for the Blackhawks were D Adrian Aucoin (groin), RW Peter Bondra (shoulder), C Michael Handzus (knee) and LW Martin Havlat (shoulder).