Turco improved to 2-9-5 against Detroit, and Dallas improved to 9-1 in its past 10 games.
Turco preserved the shutout with 48.8 seconds left, falling on his back to make a sliding stop on Detroit's Brett Lebda. Turco also denied Johan Franzen with 34.8 seconds remaining.
Hagman scored the game's only goal at 3:13 of the third period, notching his career-best 21st of the season from a sharp angle to the left of Detroit's third-string goaltender Jimmy Howard.
Howard started after Chris Osgood lost his four previous starts. Dominik Hasek is out with a hip injury.
PENGUINS 4, SABRES 1
In Buffalo, N.Y., Evgeni Malkin had a goal and assist, and Ty Conklin stopped 36 shots in leading Pittsburgh over Buffalo.
Petr Sykora had a goal and assist while Jarkko Ruutu and Colby Armstrong also scored in a victory that moved the Penguins into a tie with idle New Jersey atop the Atlantic Division standings.
Conklin, who improved to 15-4-3, played a key role by stopping the first 25 shots he faced, allowing the Penguins to build a 2-0 lead midway through the second period.
BLACKHAWKS 2, AVALANCHE 1
In Chicago, Patrick Lalime stopped 21 shots, and defenseman James Wisniewski had two assists in Chicago's win over Colorado.
Martin Havlat also scored for the Blackhawks, who won their third game in a row and are 4-0-1 in their past five.
Lalime lost a bid for his first shutout this season with 2:25 left in the third when Colorado's Jaroslav Hlinka scored.
RANGERS 3, SHARKS 1
In New York, Chris Drury scored a power-play goal and added an assist, and Henrik Lundqvist made 29 saves for the New York Rangers in a victory over San Jose Sharks.
Drury helped set up Ryan Callahan's first-period goal to tie it before sending the Rangers on their way to back-to-back victories with a goal in the second.
Jonathan Cheechoo had the lone goal for the Sharks, who have the fewest road losses in the NHL (17-6-3).
BLUES 5, BLUE JACKETS 1
In St. Louis, Brad Boyes' 31st goal snapped a five-game point drought, Eric Brewer had a career-best four assists, and St. Louis scored three power-play goals in a victory over Columbus.
Columbus' Rick Nash scored shorthanded for his 31st goal.
Andy McDonald netted his 100th career goal and defenseman Matt Walker scored his first in 153 career games for the Blues.
The Blues have won three of four and tied Columbus for 11th place in the Western Conference.