The Jets scored two running touchdowns and four field goals to claim the six-point victory, Rex's seventh in 10 meetings with his brother, who is the New Orleans' defensive coordinator.
"All right, I beat my brother again. Just kidding. Yeah, there's a little extra, but at the end of the day, now you realize that your bro just took a loss, so that's the tough thing. I pull for them every single week except one," Ryan told The AP.
"We didn't know how we'd win and all that, but we told our team, 'All I know is we've got a team that believes and fights until the end and we find a way'. And that's really what we did."
The Jets have won every other week so far this season and now have a 5-4 record to sit second in the AFC East.