Ryan Dzingel and Connor Brown each had a goal and an assist for the Senators (13-22-4), who have lost three of four. Anton Forsberg made 42 saves.
"We turned way too many pucks over, we weren't desperate enough. We battled back, too little too late," Ottawa coach D.J. Smith said. "That's a desperate team over there and we weren't ready when the game started. Maybe to be expected after an emotional game, but we just had too many guys not going tonight."
Dubois gave Winnipeg a 1-0 lead at 2:10 of the first period when he took a pass from Blake Wheeler and scored on a snap shot from the right circle.
"He's a great passer, so he makes it easy out there sometimes," Dubois said. " … He sees the ice so well that I just have to get into that open space and it's more often than not on my blade. He just makes it really easy for me out there."
Adam Lowry scored with a wrist shot from the left circle to make it 2-0 at 4:19 of the second, but Dzingel cut it 2-1 near the right goal post 29 seconds later at 4:48.
Dubois one-timed Copp's feed for a power-play goal at 8:38 of the second to give Winnipeg a 3-1 lead.
Copp has scored 11 points (seven goals, four assists) in his past nine games.
"Nothing is ever given to Andrew, and he's developed his game," Jets coach Paul Maurice said. "[He's] really worked hard on becoming an offensive player and he's always had that defensive gift. … He's worked on his hands, he's worked on making plays."