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.
Dallas scored three consecutive goals in the third to erase a 3-1 deficit.
Williams tied the game before netting the winner to give Chicago its first victory 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 victory this time. Chicago last won in Dallas on March 7, 2001 -- back when the Stars played at Reunion Arena.
"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.
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.
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.
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.
- The Stars have scored a first-period goal in nine consecutive games.
- Chicago had killed its first 19 power plays on the road before Zubov's goal.