Modano, who had a goal nullified earlier, scored at 8:33 of the third when Dallas had a 5-on-3 advantage. He scooped up a rebound off a shot from Eric Lindros and beat Vancouver's Roberto Luongo. Niklas Hagman scored the Stars' first goal 2:24 into the first.
Dallas (8-1-0) topped the mark it set in 1971 when the franchise was in Minneapolis. It was 7-1-1 that season.
Luongo had 24 saves for Vancouver.
Vancouver's Daniel Sedin scored on the first shot of the game. But that was all the Canucks could muster against Turco, who came into the game with the league's best goals-against average.
Turco (7-1-0) is also tied for the NHL lead in wins. He got some help late from Sergei Zubov.
With the puck behind Turco, Dallas' Zubov stuck his stick out and stuffed Ryan Kesler's rebound attempt before the puck crossed the red line.
The Canucks did not score in the third despite having four power plays, including two in the first six minutes.
The Stars have won 11 of their past 14 over the Canucks and five in a row at home.
Modano's goal was set up when Kesler and Kevin Bieksa were called for penalties 20 seconds apart.
Dallas got four shots off before Modano scored the winner.
Both teams scored on their first shots of the game.
Henrik Sedin dropped a nice pass in front of the net for Daniel Sedin, who easily beat Turco at 1:46 of the first. It was his fifth goal of the season.
The Stars answered 38 seconds later on Hagman's goal.
Hagman floated a shot past Luongo from the point. On Hagman's shot attempt, he knocked the stick out of the Bieksa's hand. The stick landed just to Luongo's right.
Modano had a goal nullified midway through the second when officials called Jere Lehtinen for a hand pass.
Notes: There was an announced attendance of 16,639, but a little more than half of the seats were occupied. Monday's night's game between the Dallas Cowboys and the New York Giants was being played a few kilometres away in Irving. ... Hagman's third goal of the season gave him 100 career points. ... Vancouver's Markus Naslund has 99 power-play goals - three shy of the franchise record.