"They're a great team and they've got some great players but we did a good job of being persistent," Peverley said.
Todd Bertuzzi and Pavel Datsyuk each had a goal and an assist, and Adam Almquist got his first career goal for Detroit, which lost its fourth straight at home. Henrik Zetterberg had three assists. Howard made 24 saves.
"It's a tough loss. We did a lot of good things. We played good enough defensively," Zetterberg said. "I don't think they created that many chances, I think we created more."
Eakin's power-play goal at 18:50 of the third, with Lehtonen pulled to make it a 6-on-4 advantage, tied the game at 3. It was Eakin's fourth goal and came on a wrist shot from the right circle.
"In last minute, down one. Thinking, 'Get it to the net,'" Eakin said.
Detroit's Justin Abdelkader was in the penalty box for goaltender interference after being called with 2:44 left in regulation as he ran into Lehtonen after getting off a shot.
"I would think any penalty 200 feet from home isn't a good one. All you've got to do is flip it into the corner and grind some time off of the clock. That's good for you," Detroit coach Mike Babcock said.
"What you can't do is take a penalty in any spot at that time of the game unless it's going to save a goal. That was a tough one for us obviously. It wasn't his intention to hurt the team in any way, but it's a lesson learned."
Datsyuk's goal with 8:26 left in the third gave Detroit a 3-2 lead. He made a nice move past Horcoff in the slot before firing a wrist shot past Lehtonen. It was Datsyuk's seventh goal.
Benn tied the game at 2, 4:08 into the third with a spectacular individual effort.
He stole the puck from the Red Wings' Darren Helm in the neutral zone, circled back to his own blue line and went end to end, made a move past Detroit defenseman Niklas Kronwall, and put a backhand past Howard for his sixth goal.
"Pretty lucky. ... I didn't even see the net when I let the backhand shot go. Found a hole," Benn said.
Horcoff put the Stars on the scoreboard at 19:39 of the second period when he was left alone in front of Howard. It was Horcoff's second goal.
Bertuzzi opened the scoring 7:44 into the second period with his fifth goal. His one-time slap shot from the high slot area, which deflected off the stick of Dallas' Ryan Garbutt, beat Lehtonen.
Almquist, a rookie defenseman playing in his second NHL game, made it 2-0 with 5:10 left in the second. He scored on a one-time shot from the slot.
Detroit RW Johan Franzen missed his third game with an upper-body injury. ... Dallas GM Jim Nill was formerly the Red Wings' assistant GM. It was his first game in Detroit in his new position. ... Detroit RW Jordin Tootoo cleared waivers earlier Thursday but remains with the team. ... Horcoff played collegiately at Michigan State. ... Red Wings backup G Jonas Gustavsson came off injured reserve, where he was because of a stiff neck, on Thursday. Detroit also sent G Jared Coreau to its AHL affiliate in Grand Rapids on Thursday. .. Dallas C Tyler Seguin was helped off the ice with a bloody face in the third period after colliding with two teammates. He played junior hockey with the suburban Detroit-based Plymouth Whalers of the Ontario Hockey League.
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DETROIT, MI - NOVEMBER 7: Justin Abdelkader #8 of the Detroit Red Wings sprays goalie Kari Lehtonen #32 of the...