Turco, the former University of Michigan star who came into the game with a 3.41 goals-against average, made 29 saves in the final two periods against the Central Division-leading Red Wings.
He also came into the game with a 2-10-5 mark against Detroit.
"Marty's track record is what is," Dallas center Mike Modano said. "Every year you can rewrite those records and improve on them. They're a relentless team that keeps coming at you. There were many challenging saves made."
Brett Lebda's goal in the first period gave Detroit a 1-0 lead.
Wandell, who had his first NHL goal in his second career game, and Brunnstrom scored in a 1:40 span in the second period to give the Stars the lead. Mike Ribeiro added an empty-net goal to help last-place Dallas win for the fourth time in six games.
Ty Conklin, making his third straight start for Detroit, stopped 21 shots.
"Every time we've come in here in the last few years it's always a battle for first place or a Stanley Cup playoff game," Detroit coach Mike Babcock said. "We knew we were going to have a battle. That's a proud team."
Wandell, who made his NHL debut Wednesday against Phoenix, scored at 5:47 of the second to tie it at 1. Off a Red Wings' turnover in their own zone, the 21-year-old rookie put a shot past Conklin from the slot.
"I really can't describe the feeling right now," Wandell said. "I have to wake up first."
Dallas took the lead when Brunnstrom scored from the high slot at 7:27.
Turco made sure the lead held up. He stopped 14 shots in the third, including a glove save on Henrik Zetterberg with less than 7 minutes left.
Dallas had only three shots in the third period.
"We had lots of good chances," Detroit's Marian Hossa said. "They played well defensively. Their goalie played well. But we've got to play 60 minutes and not 40, not 30."
Lebda took a pass from Jiri Hudler and beat Turco from the right circle at 6:05 of the first to put the Red Wings ahead 1-0.
Dallas had chance to tie with a 5-on-3 advantage for the final 1:31 of the first. Conklin made two big stops as the Stars did not capitalize on the power play.
Stars D Stephane Robidas (oral surgery) was scratched. Robidas was hit in the face by a puck Wednesday night. ... Detroit's
Daniel Cleary, who had an assist, has eight points in his last five games.
Copyright by STATS LLC and The Associated Press
Arena: American Airlines Center Location: Dallas, Texas
Referees: Stephane Auger, Brad Watson Linesmen: Brad Kovachik, Thor Nelson
Attendance: 18,532 (100.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Brett Lebda (2)
Assists: Jiri Hudler, Daniel Cleary
Tom Wandell (1)
Assist: Landon Wilson
Fabian Brunnstrom (9)
Assists: Mike Ribeiro, Darryl Sydor
Mike Ribeiro (4)
(Empty Net) Assists: Landon Wilson, Matt Niskanen