The Jets won their end of a home-and-home series with Washington after losing a 4-3 in a shootout Tuesday night.
Winnipeg moved back into playoff position with the win (33-27-6), giving them 72 points on the season.
Dimitri Kulikov also scored for the Jets.
Connor Hellebuyck made 33 saves for Winnipeg to earn his 5th shutout of the season.
Ilya Samsonov stopped 29 shots for Washington, who dropped to 39-18-6. The game got off to a rough start for the Jets, who lost winger Patrik Laine early in the the first period when a Michael Kempny shot careened off his foot.
He left the game and did not return.
Dimitri Kulikov scored 6:33 into the contest, beating Washington goaltender Ilya Samsonov blocker side with a slap shot from the point after Blake Wheeler hit him with a crisp pass from the right side boards.
The goal was his 2nd of the season.
The Jets got a two-man advantage just over two minutes later when Radko Gudas was assessed a penalty for high-sticking just five seconds after Brenden Dillon went off for hooking.
Winnipeg failed to score and left the first with a one goal lead.
There was no scoring in the second period.
Washington failed to score on either of the late power plays they garnered in the second.
Kyle Connor gave the Jets a two-goal lead 7:20 into the third when Mark Scheifele beat Capitals defenceman Michal Kempny in a battle behind the net before feeding Connor in the slot.
The Jet winger made no mistake, firing the disc past Samsonov to score his 32nd goal of the season.
Winnipeg visits Edmonton on Saturday while Washington travels to Minnesota for a Sunday matchup.
SHOTS-WASHINGTON 34 WINNIPEG 32