Hughes and Yegor Sharangovich scored 2:22 apart in the third period to give New Jersey a 4-2 lead. Hughes made it 3-2 at 4:28 on a rebound at the right side of the net, and Sharangovich redirected a point shot from Ty Smith at 6:50.
"You need your best players to make a difference for you and Jack made a difference for us," Devils coach Lindy Ruff said. "Coming back from a real tough injury (dislocated shoulder), I think it takes a little bit of time to get back in rhythm, but I thought he did a lot of great things.
"I know it was a three-point night, but he could've been in on a couple more opportunities. We count on him for a lot."
Dougie Hamilton gave New Jersey a 1-0 lead on the power play, one-timing a pass from Hughes from the point at 4:43 of the first period.
Bratt made it 2-0 at 11:48 on a rebound of P.K. Subban's point shot that bounced to Bratt in the slot before he skated to the goal line and lifted it over Luukkonen.
Thompson ended a 10-game goal drought when he tipped in Alex Tuch's shot from the point 33 seconds into the second period to cut it to 2-1.
Tuch was activated from injured reserve (shoulder) and made his Sabres debut after being acquired from the Vegas Golden Knights on Nov. 4. Tuch grew up a Sabres fan in Syracuse, New York.
"It was a dream come true," Tuch said. "You know, we didn't get the result we wanted tonight and that was my biggest concern, not only playing for the Sabres but trying to get a win with the guys in the locker room. We were really disappointed.
" … But, you know what, the first game's out of the way now. We can just focus on playing hockey and getting those jitters out of the way."
Thompson tied it 2-2 at 3:17 of the second. Rasmus Dahlin (two assists) stole the puck from Jesper Boqvist in the Sabres end and lobbed a pass to Thompson for a breakaway.
"We would have liked to eliminate the breakaways and the 2-on-1s," Hughes said. "We know that the other team's going to score at some point, but we want to eliminate the self-mistakes. I think tonight if you look at the first and third, we played really well, and we've got to continue to do that and try to do that for 60 minutes."