The Jets, paced by Evander Kane's two goals, scored four unanswered goals in a 4-1 win over the Caps.
Alexander Semin gave Washington an early 1-0 lead, but Kane's first goal about four minutes later opened the floodgaes for Winnipeg. Kane, Blake Wheeler and Kyle Wellwood scored within a four-minute span in the second period to put the game out of reach.
Michal Neuvirth made 27 saves, while Ondrej Pavelec made 31 of his own for the victory. Dating back to last season, the Jets have now won five straight against the Caps.
The Caps and Jets will meet again Wednesday at Verizon Center, but the Caps head to Toronto Saturday to face the Maple Leafs at Air Canada Centre.