Leason gave Anaheim a 2-1 lead at 7:51 on a rebound after Leo Carlsson split two defenders and got off a shot from in close.
Wilson scored on a breakaway coming out of the penalty box for the second time to tie it 2-2 at 15:54.
"I was a little [ticked] off at myself after the couple penalties," Wilson said. "I had guys all over my back, so I was just trying to get up ice and make a strong move and it went in, so I'll take it."
Wilson scored again on a power play at 18:39. Ovechkin took a one-timer from the left circle that was partially blocked by Ducks defenseman Radko Gudas. The puck continued toward the slot, where Wilson pushed it across the goal line to give the Capitals a 3-2 lead.
Nic Dowd scored 20 seconds later when he tipped in a shot by Rasmus Sandin to make it 4-2 at 18:59.
"I've been trying to tell myself to get to the net," Dowd said. "It just creates havoc. If that one doesn't go in, at least maybe you've got another chance."
Brock McGinn spun and redirected Leason's shot into the net off the rush to cut it to 4-3 at 11:45 of the third.
NOTES: Washington posted its eighth comeback win of the season, tying the Colorado Avalanche, New Jersey Devils and Toronto Maple Leafs for the most in the NHL. ... Wilson had seven shots on goal in 16:56 of ice time. … Gibson tied Jean-Sebastien Giguere for the most games played by a goalie in Ducks history (447).