Winnipeg got three even strength goals, one per period as they opened a three-game homestand with a win.
Neal Pionk, Alex Iafallo, Kyle Connor scored for the Jets.
Connor Hellebuyck made 23 saves for Winnipeg, who moved to 41-18-5.
The Jets, who have won three of their last five contests, moved to within two points of the Central Division leading Dallas Stars, who have 89 points.
Charlie Lindgren turned aside 26 shots for Washington, who dropped to 30-24-9 on the season.
Neal Pionk opened the scoring just over the halfway mark of the first period when he took a cross ice feed from Mason Appleton before moving in and beating Caps goaltender Charlie Lindgren blocker side just inside\ the left post with a wrister to make it 1-0 Jets at 10:05.
The goal was his 5th of the season.
Alex Iafallo tipped a Josh Morrissey point shot past Lindgren 8:16 into the second stanza to give the Jets a 2-0 lead.
Morrissey cut for the center of the ice before floating a wrister toward the net which Iafallo managed to redirect about ten feet out from the goal crease.
The goal was his 9th of the season.
Kyle Connor and Mark Scheifele broke in on Lindgren on a 2-on-1 rush halfway through the third when Scheifele fed the winger a hard pass which Connor slid past Lindgren to give Winnipeg a 3-0 lead at 10:00.
The goal was his 27th of the season.
Both clubs next see action on Wednesday as Washington visits Edmonton while Winnipeg hosts Nashville.
SHOTS-WASHINGTON 23 WINNIPEG 29
ATTENDANCE-13,716