Josh Morrissey and Mason Appleton also scored for the Jets, who bounced back after dropping their last outing 5-3 to an upstart Buffalo Sabres.
Connor Hellebuyck made 27 saves for Winnipeg, who moved to 49-19-4.
Andrew Mangiapane and Alex Ovechkin scored for the Eastern Conference leading Capitals.
Logan Thompson turned aside 22 shots as Washington, who dropped to 48-16-8.
Josh Morrissey opened the scoring 6:50 into the opening stanza when he took a Mark Scheifele feed just inside the Capitals blue line before beating Thompson with a slapshot through traffic just inside the right post.
The goal was his 12th of the season.
Andrew Mangiapane got Washington on the board with a late first period tally when he worked a give-and-go with Jakob Chychrun before wiring a wrister past Hellebuyck, beating the Jet netminder blocker side from a sharp angle at 19:20.
The goal was his 14th of the season.
Mason Appleton converted a cross ice feed from Nino Niederreiter snapping a high wrister past Thompson beating him glove side to give the Jets a 2-1 lead at 19:20 of the second period.
The goal broke a thirteen game scoreless skid for the Jet winger.
Alex Ovechkin scored at the 16 minute mark, beating Hellebuyck with a low wrister after Aliaksei Protas hit him with a pass just inside the left faceoff dot.
The goal was his 36th of the season and 889th of his NHL career, leaving him with six more to best Wayne Gretzky's record of 894.
The game went to overtime.
SHOTS-WASHINGTON 29 WINNIPEG 25
ATTENDANCE-15,225
