Williams scored his second goal with 20.4 seconds left and the Blackhawks snapped a nine-game losing streak in Dallas, beating the Stars 5-4 on Wednesday night.
Dallas scored three straight goals in the third to erase a 3-1 deficit.
Williams tied the game before netting the winner to give Chicago its first win in Dallas since 2001. He also beat the Stars with an overtime goal Oct. 13.
"This time we found a way to win," Williams said. "We gave up a couple, then took the momentum back. We're making it hard on ourselves."
No one experienced a wider range of emotions than Modano.
Modano was initially awarded an assist on Sergei Zubov's power-play goal in the third for his 1,232nd point, matching Phil Housley for the most points by an American-born NHL player. After the game, it was ruled Modano never touched the puck and the assist was taken away from him.
This probably explains why Modano was hesitant to acknowledge the crowd after he appeared to tie the mark. He said the official scorers shouldn't have credited him with an assist in the first place.
"Someone screwed up," Modano said. "It's partly why I didn't want to stand up. After a moment I stood to get it over with and get the game running again."
The Zubov goal at 10:07 gave the Stars a 4-3 lead, and it appeared the Stars were going to turn back the Blackhawks once again in Dallas.
But Williams made sure the Blackhawks left Texas with a win this time. Chicago last won in Dallas on March 7, 2001 - back when the Stars played at Reunion Arena.
James Wisniewski fired a long pass to Williams, who made the winning wrist shot from the right circle past goalie Mike Smith.
"It was a nice win," Chicago coach Denis Savard said. "It got everybody going. I like the way we fought back."
The Stars seemed to seize momentum when they scored three unanswered goals in the first 10:07 of the third.
Philippe Boucher's first goal of the season cut the deficit to 3-2 forty seconds into the third. Dallas evened things on Niklas Hagman's third short-handed goal of the season.
Then 12 seconds into a 5-on-3 power play, Zubov - who had assists on Dallas' two previous goals - gave Dallas the lead and Modano the apparent record-tying point.
"We lost that energy, that moment." Dallas' Brenden Morrow said.
Marty Turco, who gave up three third-period goals in a loss to San Jose on Monday, was pulled in favor of Mike Smith at 10:59 of the second after stopping 18 shots. Smith made six saves.
Nikolai Khabibulin broke a seven-game winless streak in Dallas and had 19 saves for Chicago, which snapped a three-game losing streak.
"Lose three in a row like we had, it's difficult to take," Savard said. "But this is a sign of a character team and it showed."
Mike Ribeiro and Boucher each had a goal and an assist for the Stars.
Chicago's Patrick Kane and Wisniewski also had a goal and an assist.
The Stars got on the scoreboard first thanks to a streaking Ribeiro.
Ribeiro, who has scored in seven straight, gave Dallas a 1-0 lead in the first. Jonathan Toews scored his fifth goal with help from assists by Tuomo Ruutu and Kane.
Wisniewski gave the Blackhawks a 2-1 lead in the second with a power-play goal, and Kane's tally extended the lead to 3-1.
Notes: The Stars have scored a first-period goal in nine straight games. ... Chicago had killed its first 19 power plays on the road before Zubov's goal.
|Mike Ribeiro (5) ASST: Philippe Boucher (7), Jere Lehtinen (6)|
1 - 0 DAL
|Jonathan Toews (5) ASST: Tuomo Ruutu (4), Patrick Kane (11)|
1 - 1 Tie
|PPG - James Wisniewski (3) ASST: Robert Lang (6), Dave Bolland (1)|
2 - 1 CHI
|Patrick Kane (5) ASST: Tuomo Ruutu (5), James Wisniewski (2)|
3 - 1 CHI
|Philippe Boucher (1) ASST: Brenden Morrow (8), Sergei Zubov (4)|
3 - 2 CHI
|SHG - Niklas Hagman (7) ASST: Sergei Zubov (5), Stu Barnes (5)|
3 - 3 Tie
|PPG - Sergei Zubov (3) ASST: Mike Ribeiro (8)|
4 - 3 DAL
|Jason Williams (5) ASST: Robert Lang (7)|
4 - 4 Tie
|Jason Williams (6) ASST: James Wisniewski (3)|
5 - 4 CHI
|Adam Burish Interference on goalkeeper against Marty Turco|
|Brent Seabrook Interference against Niklas Hagman|
|Rene Bourque Holding against Jere Lehtinen|
|Mike Modano Tripping against Robert Lang|
|Brent Seabrook Tripping against Jeff Halpern|
|Philippe Boucher Tripping against Patrick Kane|
|Jonathan Toews Hi-sticking against Mike Modano|
|Jim Vandermeer Roughing against Brenden Morrow|