EAST RUTHERFORD, N.J. — Matt Barkley had just put the finishing touches on a stunning victory when he jogged over to the sideline, found his mother in the stands and handed her his well-deserved game ball.

It was quite a moment for Barkley, the Buffalo Bills quarterback who looked nothing like a guy who had no job and an uncertain future just a few weeks ago.

Barkley ignited Buffalo’s bumbling offense with two touchdown passes, including one to offensive tackle Dion Dawkins, LeSean McCoy broke out of a season-long slump with 113 yards rushing and a pair of touchdown runs, and the Bills embarrassed the Jets, 41-10, on Sunday.

“For me, I knew I could play in this league,” Barkley said. “To get back out there after two years, it was — and I don’t want to be cliché by saying it was like riding a bike, but I’ve done this for years. I feel like I was made to play football.” He added that the game had been “an example of going out there and doing what I was made to do.”