Connor was one of five Winnipeg players with a multi-point game.
Nikolaj Ehlers had a goal and two assists, Axel Jonsson-Fjallby had a goal and assist, and Morgan Barron and Dylan DeMelo, who scored short-handed, added goals. Pierre-Luc Dubois finished with four assists and Brenden Dillon had a pair.
David Rittich stopped 34 shots for Winnipeg, which improved to 18-1-0 this season when scoring four or more goals in a game.
Bo Horvat scored his 29th of the season and J.T. Miller had a goal and two assists for the Canucks (17-19-3), who have one win in their last five games. Jack Studnicka and Sheldon Dries also scored.
Collin Delia started the game in net for Vancouver, but was replaced at 5:34 of the second period after giving up four goals on 13 shots. Spencer Martin made 11 saves in relief.
Connor scored his 18th of the season after taking a feed across the front of the net from Ehlers at 6:22 of the first period.
Ilya Mikheyev appeared to score with Vancouver's first shot of the game half a minute later, but Winnipeg successfully challenged for offside and the goal was denied.
Connor made it 2-0 after racing around defenseman Tyler Myers and beating Delia with a low shot at 7:59.
Miller got Vancouver's first goal at 15:14, followed by Studnicka tipping in a Luke Schenn shot at 17:33 to tie the game at 2.
In his second game back after missing 36 games after sports hernia surgery, Ehlers recorded his first goal of the season at 3:40 of the second period.
Barron made it 4-2 just under two minutes later, but the Canucks quickly tied it up.
Horvat blasted a shot past Rittich at 7:05 and Dries redirected a shot by Miller during the game's first power play at 9:26. Horvat has three goals and two assists in a four-game point streak, and 13 points in his past seven games.
A high wrist shot by Jonsson-Fjallby with 1:43 left gave the Jets a 5-4 edge.
Vancouver got a second power play early in the third, but DeMelo scored short-handed at 5:29 after taking a drop pass from Jonsson-Fjallby.
Connor completed his hat trick at 13:42.
NOTES: Connor and Dubois are riding six-game point streaks. Connor has five goals and six assists in his run, while Dubois has four goals and six assists. ... Connor extended his home point streak to 11 games, collecting nine goals and 12 assists during that span. Ehlers holds the franchise record with points in 12 consecutive games at home last season. Josh Morrissey had his 10-game home point streak end.
Canucks: At Pittsburgh on Tuesday in the second game of a four-game trip. Jets: At Detroit on Tuesday in the first game of a three-game trip.
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