Paul Postma also had a goal and three assists in the split-squad game before a jubilant crowd of 15,004 at MTS Centre. Columbus won the matchup in Ohio 5-1.
The Jets raised their sticks to the screaming crowd as they left the ice.
Scheifele was Winnipeg's seventh overall pick in this year's NHL draft.
Columbus got its lone goal from Ryan Johansen.
In Winnipeg, fans were chanting "Go Jets Go" before the players even stepped on the ice.
And when they did, they were greeted by a standing ovation and loud singing of the Canadian national anthem.
It was a long-awaited moment for the fans.
The Jets left Winnipeg after the 1995-96 season to become the Phoenix Coyotes, leaving fans to adopt the American Hockey League Manitoba Moose that fall.
When the announcement came last May that Moose owner True North Sports and Entertainment had purchased the Atlanta Thrashers and was moving them to the Manitoba capital, it sent the city into a frenzy of anticipation.
Even the game's first fight 37 seconds into the first period got the fans roaring as Byfuglien went at it with Cody Bass.
Byfuglien, who's facing four charges in Minnesota related to impaired boating, led all NHL defensemen in goals last season with 20 and added 33 assists.
Postma opened the game's scoring at 7:49, getting the puck past Blue Jackets goalie Curtis Sanford, who stayed in for the full game.