Mike Modano found the opening he was looking for.
Vanbiesbrouck stopped 24 shots, including close-range attempts by Mike Keane in the first period and Modano in the third.
"When you give up a goal with 30 seconds left, you're certainly not too elated," Vanbiesbrouck said.
"We did a pretty good job all night against a pretty good power play. It was kind of a fluky goal. They poked at it and I got my pad on it, but not enough to keep it out of the net."
Dallas outshot the Flyers 3-2 in overtime, but the Flyers missed the best opportunity when Daniel McGillis fired wide of the goal from the slot.
"I thought 'Mo' really answered the bell," Dallas coach Ken Hitchcock said about Modano. "He was a strong player every shift. To play head-to-head against Eric Lindros is a big challenge for anybody."
Daymond Langkow scored a first-perod goal for the Flyers, 4-0-1 in their last five home games and 10-2-2 since opening the season 0-5-1 the worst start in franchise history.
"It was a tough loss of a point," Philadelphia coach Roger Neilson said. "Especially when we checked as well as we did the whole game. But that's the way it goes. You just hope that things even out."
Langkow scored his fourth goal of the season at 4:56 of the first period, taking a centering pass from Chris Therien near the boards and lifting a wrist shot over Belfour.
Belfour, recovering from a strained groin, made 19 saves for the Stars, who stopped the NHL's best power play in four attempts.
"I think we played really well defensively all night," Hitchcock said. "We played a real strong third period to give ourselves a chance, not letting the game get away from us."
The Stars were again thwarted in their bid for the franchise's 1,000th victory. They won 758 games in 26 seasons in Minnesota, and 241 games since moving to Dallas seven years ago.
©1999 The Associated Press. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed