DETROIT - Pavel Datsyuk stickhandled around a defender and sent a perfect pass across the front of the goal.
All Valtteri Filppula had to do was shoot into an open net, and he had no problem scoring his second goal of the game.
"Whenever he has the puck, you can always expect it's going to come your way," Filppula said. "I've obviously played with him for a while now, but still, every once in a while you get surprised."
All six of Dallas' previous games this season were decided by one goal, but the Stars couldn't keep this one close in the third after playing at Columbus the previous night.
"Saw some good things here coming off back to back, like the shot clock," Dallas coach Glen Gulutzan said. "See some good things coming."
Jimmy Howard made 25 saves for Detroit, which outshot Dallas only 27-26.
Zetterberg scored on a two-man advantage in the final minute of the second period to give the Red Wings a 2-1 lead, and Brunner and Filppula scored 23 seconds apart in the third.
"I just expected him to get out and forecheck, but he took it upon himself to have a couple bouts," Red Wings coach Mike Babcock said. "We don't mind that either, but we'd just as soon he forecheck. He's a guy that gives us a different dimension than we've had, and he's physical out there, and guys know he's out there."
The 5-foot-9 Tootoo was giving up 6 inches in his fight with Dillon.
"Basically just trying to protect myself from getting hit — and just keep whaling," Tootoo said.
The Stars had a two-man advantage for 39 seconds late in the first but couldn't convert, and the period ended scoreless. The Red Wings have not scored in the first period all season.
Eriksson gave the Stars a 1-0 lead, lifting a rebound over Howard, but Filppula tied it later in the second when Datsyuk found him in front of the net.
Dallas was hurt late in the period by a pair of high-sticking penalties. Jamie Benn was given a double-minor with 3:41 remaining, and although Zetterberg went off 41 seconds later for tripping, Ray Whitney took a penalty for the Stars with 2:18 to play.
The end result was that the Red Wings had a 5-on-3 once Zetterberg's penalty was over, and the Detroit captain took advantage for the go-ahead goal, beating goalie Kari Lehtonen with a slapper to the upper-right corner.
Lehtonen came within 3.4 seconds of a shutout in a win at Detroit last week, but he made only 21 saves this time and was pulled with 4:30 remaining in the game.
Brunner made it 3-1 in the third when he deflected a shot from the point past Lehtonen. Although there was some question as to the height of Brunner's stick when he touched the puck, the goal stood.
Datsyuk then manoeuvred around a defender and sent another nice pass to Filppula, who scored easily with Lehtonen out of position.
NOTES: Red Wings F Darren Helm was scratched with back inflammation, an ailment that is expected to improve with medication — instead of surgery that would've put him out of the lineup for a much longer period of time. ... Jaromir Jagr's assist on Eriksson's goal was his first point since a two-goal, two-assist game against Phoenix in the season opener.