Taylor Raddysh cut the deficit to 3-2 at 4:54, scoring from a sharp angle below the left circle.
Morrissey made it 4-2 at 1:10 of the third period, scoring on a wrist shot from the high slot off a pass from Scheifele behind the goal line.
Wilson pulled the Capitals within 4-3 at 7:26, scoring on the rebound after Hellebuyck made a pad save against Dylan Strome in front.
“I think once we got our feet under us and we started playing the right way, it was a heck of a hockey game,” Wilson said. “I think we kind of game them the first period, but after that it was two of the best teams, I think, just kind of going toe-to-toe. They made a good play there in overtime, and it made the difference.”
NOTES: Ovechkin has scored 56 goals in 74 games against the Jets/Atlanta Thrashers, the most against any opponent. … Ovechkin has six goals in his career against Hellebuyck. … Winnipeg ended an 11-game losing streak (0-7-4) in Washington, winning for the first time since Jan. 22, 2013 (4-2). … Scheifele has 60 points (31 goals, 29 assists) in 54 games, his 10th career 60-point season, which surpassed Blake Wheeler (nine) for the most in Jets/Alanta Thrashers history.