The win was the Red Wings' third in as many games that Clark and defenseman Chris Chelios have played for Detroit since being acquired in trading deadline deals Tuesday.
"We had a good team before and we have to be a better team now," said Detroit forward Sergei Fedorov, who assisted on Clark's game-winner.
"It's been a good three games," Chelios said. "A solid three games."
"The puck was laying there. It was not that hard to put in," Clark said. "It was something where the guys put the puck to the net and I was just able to be in the right spot at the right time."
There was a lengthy video review after the goal because Clark was close to the crease, but the puck was already in the crease when he got there and the goal counted. Earlier, the Flyers had a goal disallowed because a payer was in the crease.
"It's a touchy rule now. We're always very close," Clark said. "When something happens so quick, it's tough to say whether you're in or out. It's usually pretty close when the puck gets around the crease there."
The loss ended a three-game winning streak for the Flyers, who played without all-star center Eric Lindros. He was suspended for two games by the NHL for a high-sticking incident Saturday with Petr Nedved of the New York Rangers.
"We've got key players out," said forward Mikael Renberg, who scored one of the Flyers' goals. "That's not good, but even without them we played well and you have to take something out of it."
Both goalies were superb as Detroit's Chris Osgood stopped 24 shots and Vanbiesbrouck 28.
Kozlov scored the only goal in the first period when he batted Larry Murphy's rebound past Vanbiesbrouck on a power play at 8:31.
LeClair made up for it with an assist on Renberg's tying goal 9:52 into the third. Renberg poked the puck in off Osgood's right pad during another scramble in front of the net.
Kozlov scored his second goal by redirecting Aaron Ward's centering pass through Vanbiesbrouck's legs at 9:32. But the Flyers regained a tie on a power play at 11:44 when Jones took a centering pass from Steve Duchesne and beat Osgood on his stick side.
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