The Jets (1-1-1), who had scored just twice in two opening defeats, fell behind 1-0 to Washington before Evander Kane and Andrew Ladd netted power-play goals to give the visitors a 2-1 lead in the first period.
Blake Wheeler and Jim Slater padded the Jets' lead to 4-1 in the second before Troy Brouwer scored a consolation goal late in the third. Ondrej Pavelec made 32 saves for the win.
"I thought it was a really solid effort from start to finish," Ladd said. "We had four lines going and we were smart with the pucks. That's the way we want to play."
Alex Ovechkin assisted on a first-period goal to Matt Hendricks for Washington (0-2-0), who suffered a 6-3 loss to Tampa Bay in their season-opener on Saturday.
Ovechkin, a two-time Hart Trophy winner, has yet to score this season as the Capitals have been dominated in the early going - a tough start for Washington's new coach Adam Oates, a former Capitals player who has been given his first head coaching job.
Washington's loss was their first home opening defeat since 2000, a game against the Los Angeles Kings that featured an assist from Oates.
Braden Holtby stopped 35 Winnipeg shots but it was not enough to get the Capitals in the win column.
"It's two games out of 48," said Washington forward Joel Ward. "We are just focused on the next day and the next game."