"We talk a lot about getting the puck to our speed guys in open ice," Athanasiou said. "I got a good bounce and was able to get a goal on our first shift. That's always a good feeling."
Athanasiou has four goals on 21 shots in his past four games.
"We showed our guys video of what he did to Ottawa before the game, but Aaron tried to get a 50-50 puck and missed, and once he gets behind you, he's gone," Florida coach Bob Boughner said. "That's their game plan: Throw it to him deep and let him use that speed."
Tatar gave the Red Wings a 2-0 lead at 7:08 of the second period off a pass from Athanasiou.
Mike Matheson made it 2-1 with two seconds left, taking a pass at center ice and using a spin move to get past Green.
"I threw an outlet pass out of our zone, and then I saw a lot of open ice, so I decided to go for it," said Matheson, who scored in overtime to defeat Detroit 2-1 on Dec. 11.
Barkov tied it 2-2 at 3:19 of the third period, finishing a 2-on-1 by tapping in Jonathan Huberdeau's pass for his 12th goal, first since Dec. 14.
Florida on Thursday had its game at the Boston Bruins postponed because of weather and did not fly to Detroit until Friday morning.