Mike Ribeiro of the Stars (6-1-0) tied the score 4-4 with 1:14 remaining from the slot off Niklas Hagman's centring pass.
The game seemed headed for overtime when Philippe Boucher's shot from the point got past Chicago goaltender Brian Boucher in the final minute as Dallas' Jeff Halpern set a screen in front of the net.
The 1996-97 Stars also won six of their first seven games.
Martin Lapointe had given the Blackhawks a 4-3 lead with 4:31 left, but the Stars came back to continue their dominance over Chicago, improving to 13-0-1 in the teams' last 14 meetings.
The Blackhawks' last victory over the Stars was on Jan. 20, 2002, while their last win in Dallas was on March 7, 2001.
Dallas trailed 3-1 and showed little life, but the Stars tied it on Mike Modano's power-play goal with 6:19 left and Jere Lehtinen's even-strength goal with 5:34 remaining.
Rene Bourque and Michael Holmquist scored power-play goals and Lasse Kukkonen added one at even strength for the Blackhawks (4-3-0).
Antti Miettinen also scored for the Stars and Marty Turco made 18 saves for Dallas.
Miettinen's deflection off a setup from Stu Barnes at 4:05 of the first period gave Dallas a 1-0 lead.
Chicago tied it on Kukkonen's blast from the left point at 15:51, six seconds after a Blackhawks power play had expired.
The Blackhawks grabbed a 2-1 lead on Bourque's power-play goal at 17:41 of the first period.
Hagman was awarded a penalty shot at 5:34 of the second period, and he appeared to beat Brian Boucher before his shot bounced off the crossbar.
Holmquist's power-play goal at 19:40 of the second period extended Chicago's lead to 3-1.
Notes: The Stars announced the signing of LW James Neal to a three-year contract. Neal, currently playing with the Plymouth Whalers in the Ontario Hockey League, was Dallas' second-round selection in the 2005 entry draft. The six-foot-three, 200-pounder had 21 goals and 37 assists for Plymouth last season. ... Chicago, which started Friday leading the league in first-period goals with 12, got two more. ... For the game, Dallas had only two shots during a total of 3:40 with a two-man advantage.