Hasek was hardly challenged by Minnesota's stagnant offence all night, and Dan Cleary, Niklas Lidstrom and Mikael Samuelsson scored against the Wild, who were shut out for the first time since Nov. 1, 2005, a span of 93 games that was the second-longest streak in the NHL behind Detroit's 144.
The Wild lost for the 11th time in 15 games and have been in a free fall since starting the season a franchise-best 6-1. Injuries have crippled them over the last month, with high-flying winger Marian Gaborik missing his 18th straight game with a groin injury.
Pavol Demitra has been out since Nov. 20 with a head injury and veteran Wes Walz is also missing with an injured hip flexor.
Another sign that luck isn't on Minnesota's side? Defenceman Kurtis Foster was hit in the throat by a puck, while sitting on the bench in Wednesday night's loss to San Jose and is expected to miss extended time.
Gaborik has been skating in practice all week and can't get back a moment too soon for the Wild, who have managed just 36 shots on goal in their last two games.
Manny Fernandez made 20 saves for the Wild and fell to 1-8 in his last 11 starts after beginning the season 8-1.
The Red Wings haven't had the same injury problems, but they're still getting used to playing without former captain Steve Yzerman, who retired after giving Detroit 22 seasons of gritty leadership.
Lidstrom has taken over as captain and is the only defenceman in the league to lead his team in scoring. He had a goal and an assist Friday night to give him 21 points on the year, but the Wings entered the week on a five-game losing streak.
They snapped the skid with a 2-1 victory over Dallas on Monday, and took advantage of Todd White's hooking penalty in the second period to get out in front against Minnesota.
Just as White was getting out of the box, Cleary slipped in from the point to the slot, and Robert Lang found him all alone in front for his seventh goal of the season.
Cleary crumpled to the ice immediately after beating Fernandez high on the glove side on a play that proved disastrous for Minnesota. Pascal Dupuis was issued a double minor for high-sticking when he struck Cleary.
The Red Wings were on the board again 37 seconds later when Lidstrom ripped a slap shot from the left point. Henrik Zetterberg's timing was perfect as he slid across the crease to screen Fernandez, who didn't see the shot until it was in the net for a Detroit 2-0 lead.
That was more than enough for Hasek, who barely broke a sweat in this one, but was good when he had to be.
Just under four minutes into the second period, Hasek's stick broke during a scramble in front of the net. Seconds later, Pierre-Marc Bouchard broke in all alone, with Hasek just wielding the shaft of the stick.
But he put himself in good position to stop Bouchard's first shot, then smothered the rebound to keep Minnesota off the board.
Notes: Wild D Shawn Belle made his NHL debut. ... Red Wings C Jason Williams (leg) and F Johan Franzen (concussion) did not play. Both were listed as day-to-day. ... Wild coach Jacques Lemaire said Gaborik will not play on Saturday at Dallas.