With Nashville's 3-2 overtime win over New Jersey, however, the Jets remain in the Central Division cellar.
Zach Bogosian and Michael Frolik also scored for the Jets (26-25-5). Captain Andrew Ladd picked up two assists.
Alexander Edler, Ryan Kesler and Jason Garrison scored for the Canucks (27-20-9). Daniel Sedin picked up an assist but his goal-scoring drought continued and now has stretched to 15 games.
It was the last game Vancouver has to play without head coach John Tortorella behind the bench as his suspension ends.
The Jets outshot the Canucks 15-7 in the first period and Vancouver had managed just one when Bogosian scored from the point at 5:02, slamming one past backup Eddie Lack's glove. The Canucks rested Roberto Luongo Friday night.
The Jets kept up the pressure and Vancouver called a time out just over a minute later as Setoguchi backhanded one in from the side of the net to make it 2-0. It ended a seven-game goal-scoring drought for the left winger.
The Canucks got their first on a power play when Edler slipped a rebound behind Ondrej Pavelec from the side of the net at 10:27.
Winnipeg continued to control the play, however, and Dustin Byfuglien thought he had another with about a minute and a half left in the period but Lack caught a piece of it as the big winger swept past.
The Jets started well in the second but turned over the puck in front of their own net and Kesler was right there to backhand his 19th of the season past an unprepared Pavelec at 4:48.
The tie didn't last long. Frolik put the Jets back in the lead when he snapped in Andrew Ladd's behind the net pass at 6:41 and that was it for the second. Winnipeg kept its edge on shots at 13-10.
The Canucks tied it up again in the third when Jason Garrison blasted one from the point and Pavelec went down as the puck went high.
But Setoguchi's second of the game at 17:04 put the Jets back in the lead and the Canucks took a high-sticking penalty at the same time to keep them from getting much chance of another comeback.
It was Vancouver's third loss in a row as the Canucks struggle to hold the eighth and final playoff spot in the West.
Notes: It was Vancouver's first visit to the new Jets at the MTS Centre. The last time they played the Jets at home was in 1996, the final season for the original Jets before they relocated to Phoenix and became the Coyotes. With Vancouver's visit, every team in the NHL has now played in Winnipeg.