In a flurry of activity in front of Detroit goalie Chris Osgood, Daley took a shot that got knocked down but was still on the ice when he followed up for his fourth goal of the season -- and Dallas' only lead.
The Stars, who trailed 3-1 after the first period, forced overtime when Steve Ott scored with 3 minutes left in regulation. Ott took a crossing pass from Mike Ribeiro and knocked the puck into the left side of the net when Osgood was unable to recover.
Osgood stopped a season-high 45 shots, but couldn't save the Red Wings, whose winning streak included a 6-1 victory over Dallas last week.
Pavel Datsyuk had a goal and two assists for the Red Wings, giving him 18 points the last 11 games.
The Red Wings took a 4-3 lead with 14:41 left when Datsyuk worked the puck most of the length down the left side of the ice, shed defender Darryl Sydor and scored.
Dallas almost had a tying goal right after that but James Neal's shot hit the crossbar, bounced straight down in front of the line and was secured by Osgood after Loui Eriksson swiped and missed the puck.
Connecting you to your favorite North Texas sports teams as well as sports news around the globe.
Marty Turco had 26 saves and is now 4-11-5 in his career against the Red Wings.
In the loss at Detroit on Thursday night, Turco was pulled after two periods. He then allowed goals on consecutive shots midway through the first period Monday night.
Brian Rafalski scored from just inside the blue line, getting the puck past a screened Turco to start the scoring. Less than 2 minutes later, Datsyuk made a backhand pass to Tomas Holmstrom, who had an open net for a 2-0 lead.
The Red Wings led 3-1 when Marian Hossa, set up by the goal inside the Dallas defenders on a power play, poked a shot through Turco's skates.
Stephane Robidas scored from the top of the right circle less than a minute into the second period, but Osgood then made an incredible recovery to prevent another goal 2 minutes later.
Ribeiro took a shot from the right side toward a seemingly open net. But Osgood made a diving recovery to get his glove on the puck, sweeping it into his body and keeping it out of the net. The play was reviewed, and officials said the puck never completely crossed the line under Osgood.
Dallas tied the game 3-3 when Mark Parrish cored from the top of the circle with 4 minutes left in the second period.
Nicklas Grossman got his first career goal, only 11th point, in 110 regular season games, when got Dallas' first goal late in the first period. He scored a goal in the playoffs against Detroit last season.
Notes:@ It was Turco's 420th game for the Stars, matching Cesare Maniago (1967-76) for the most by a goaltender in franchise history. Turco was already the career leader in wins (224) and shutouts (34). ... Detroit overtook Boston for the NHL lead in goals scored at 157. ... Red Wings D Chris Chelios, who turns 47 later this month, was a healthy scratch for the third straight game.