The game also marked the return of starting goaltender Connor Hellebuyck after a 12-game absence following knee surgery.
Winnipeg only won twice in that span.
Alex Iafallo had a goal and an assist and Logan Stanley, Morgan Barron each scored for the Jets.
Adam Lowry, Josh Morrissey, Kyle Connor and Mark Scheifele each had a pair of assists.
Connor Hellebuyck stopped 22 shots for the Jets, who moved to 15-15-1.
Jakob Chychrun scored for the Capitals.
Logan Thompson made 30 saves for Washington, who dropped to 18-10-4.
Logan Stanley opened the scoring 9:14 into the contest when he batted a puck that was banked off the end boards by Josh Morrissey.
The goal was his 5th of the season.
Morgan Barron gave Winnipeg a 2-0 lead at 18:43, finishing off a 2-on-1 with Adam Lowry as he buried the captain's feed past Lindgren.
The goal was his 5th of the season.
Gabriel Vilardi made it 4-0 on a late power play goal, finishing off a neat three way passing play that he tapped in for the goal.
Vilardi scored again at 11:55 of the third on a nifty setup from Kyle Connor and Mark Scheifele, which left him alone in front of Thompson.
The goal was his 16th of the season.
Jakob Chychrun scored on the power play at 16:32, one timing a John Carlson feed past Hellebuyck to get Washington on the board.
The goal was his 12th of the season.
SHOTS-WASHINGTON 23WINNIPEG 35
ATTENDANCE-14,096
