Halpern’s goal came just 24 seconds into the contest while Lundqvist scored 45 seconds into the second period.
The shutout was Turco’s first in 24 career playoff games.
Stu Barnes collected two assists as the Stars disappointed a sellout crowd of 18,630.
Canuck goaltender Roberto Luongo made 25 saves.
The best-of-seven Western Conference quarter-final now moves to Dallas for Game 3 on Sunday (9:30 ET).
Neither team seemed to show the affects of Wednesday’s marathon 5-4 game which the Canucks won in quadruple overtime.
Dallas played with more jump and an intensity Vancouver lacked. The Stars moved the puck with authority and always seemed to have a player open for a pass or ready to ride a Canuck out of the play.
Markus Naslund might have been the best Canuck on the ice. He played with a urgency many of his teammates didn’t have, making hits and going after the puck.
Vancouver didn’t get a shot on net until 6:40 of the first. The Canucks best scoring chance of the first two periods came when Jan Bulis rang a shot off the post during a power play.
While Turco was steady he wasn’t forced to make many stellar saves. His best came when he blocked Daniel Sedin on his doorstep, then got in front of a Willie Mitchell shot, both in the third.
Halpern’s goal came on Dallas’s first shot. Defenceman Sergei Zubov fired a shot from the point that Halpern deflected past a surprised Luongo.
Dallas struck early again in the second period. Mike Modano slid a perfect backhand pass to a charging Lundqvist who beat Luongo on the short side.
Luongo had a tough first. He was slow to get up after being hit in the face by a Niklas Hagman shot, then had his mask knocked off when Antti Miettinen breezed through his crease.
Halpern’s goal set franchise playoff records for both teams.
For Dallas, it was the fastest goal to begin a game since Mike Keane scored 26 seconds into a game at home against Edmonton on April 14, 2001 and Stewart Gavin in St. Louis on April 20, 1991.
It also was the quickest goal the Canucks had allowed since Mark Messier scored for Edmonton 33 seconds into an April 10, 1986 playoff game.
With Matt Cooke (groin), Alex Burrows (suspected concussion) and Ryan Kesler (broken finger) out, the Canucks called up Jannik Hansen and Nathan Smith from the AHL’s Manitoba Moose.
Notes: Hansen played his first NHL game . . . Defenceman Brent Sopel, who missed Game 1 with back spasms, returned to Vancouver’s lineup, sending Rory Fitzpatrick to the press box . . . Henrik Sedin’s winning goal in the fourth overtime period of Game 1 was his second playoff OT winner. He also beat Detroit in OT of the first game of the 2002 playoffs . . . It was Bryan Smolinski’s 101st playoff game.