Victor Olofsson had a goal and an assist, and Luukkonen made 23 saves for the Sabres (20-18-2), who finished their four-game homestand with three straight losses.
"A really important factor for us tonight was to get back to our game, play a higher tempo, higher paced game," Buffalo coach Don Granato said. "I thought [the Jets] played with a lot of intent to try to deny that. … They were aggressive defensively. They clogged the neutral zone up very well. We had to work hard to get our ice and create our ice. I thought our guys did a nice job to do that and got some volume of opportunity.
"[Hellebuyck] was their best player tonight. On the flip side, 'Upie' didn't have as much work as that, but Upie was also very good, and his body language was good. He looked with it. He read things well and I was happy to see that from him as well."