Barkov scored at 27 seconds of the second period on a one-timer for a 3-1 lead, but Ovechkin scored a power-play goal at 6:13 to cut it to 3-2, and at 12:14 to tie the score 3-3.
Dadonov gave Florida a 4-3 lead 18:59 when he one-timed Jonathan Huberdeau's pass from behind the net on a power play.
Wilson was injured when he blocked a shot during that power play.
"I can talk a lot about Tom Wilson," Reirden said. "Tonight's game summed it up for me. He lays down, blocks a shot at the end of the second and they end up scoring. I'm not sure if he's going to be able to come back and play in the third, and he comes back, physical right away in the beginning of the third, and ends up scoring the goal to get us tied up at the time and eventually scores the winner. That's how hockey should work.
"When you want to pay the price and you want to play the game the right way, then things seem to go your way, so I'm not surprised at all to see Tom get rewarded like that."