Clemmensen made 39 saves for the Panthers, who won for the fourth time in five games to reach .500 (9-9-2). Stephen Weiss scored Florida's other goal and added an assist. Nathan Horton had two assists.
"Our goalie was our best player. He gave us a chance to hang around, and we found a way to pop one," Panthers coach Pete DeBoer said.
Some of Clemmensen's biggest saves came against Darren Helm, who had eight shots. Clemmensen stopped Helm on breakaways in each of the first two periods.
"Hopefully, tonight was a harbinger for my game getting to where I really want it to be," Florida's backup goalie said. "We had to weather a little bit there in the first. They're a great team. We had to battle so hard all night, and we really stuck with it."
"We just couldn't get the puck in, couldn't score," Red Wings defenseman Niklas Kronwall said. "We battled hard. The puck just wouldn't go in."
McCabe beat Osgood with a one-timed shot from the right circle for his third of the season, converting Weiss' pass.
Weiss tied it 1-1 at 8:13 of the third period with his seventh goal. Horton threaded the needle on a cross-crease pass, and Weiss put a shot into the open side of the net.
"We all knew we weren't playing good for the first two periods," Horton said. "We tried to come out in the third and put on some pressure."
Datsyuk's power-play goal with 2:02 left in the second period opened the scoring. He jammed in his own rebound for his fifth goal.
"We had more than enough chances," Red Wings coach Mike Babcock said. "We didn't have much puck luck."
Osgood returned after missing three games with the flu. ... DeBoer was once the coach and general manager of the suburban Detroit-based Plymouth Whalers of the Ontario Hockey League. He holds a law degree from the University of Detroit. Weiss and Panthers' teammate Gregory Campbell played with Plymouth. ... Hall of Famer Igor Larionov, who played for the Panthers and Red Wings, was in attendance. ... Florida LW Cory Stillman had to be helped off the ice after taking a hit from Brad Stuart along the boards and didn't return. "Stillman's got a knee injury and is going to be out a while," DeBoer said. ... It was Florida's second win (2-5-3) at Joe Louis Arena.