Hamilton scored a slap shot from the point through a screen to give the Devils a 3-2 lead at 15:37 of the third period.
"It's good for us to get the first win," Hamilton said. "I think that'll help us with our confidence and we'll get right back at it tomorrow (against the Arizona Coyotes at Prudential Center)."
Haula scored an empty-net goal at 18:29 for a 4-2 lead.
Fabbri scored a power-play goal on a rebound from the slot at 19:26 for the 4-3 final.
"I thought in the second period we got going pretty good for a while, there were pockets of good play," Ruff said. "I know consistently through the game we can be a lot better. I had individuals that didn't have a very good night. I can point to a lot of different players and a lot of different lines. I thought every line had something missing, so it was hard to get some continuous flow in the game when maybe two guys are going pretty good and one guy wasn't."
NOTES: Hughes is the first player in Devils history with three multipoint efforts in season openers. … Larkin had one assist, finished 13-for-21 (62 percent) on face-offs and led all skaters with six shots on goal. ... Siegenthaler had three assists in a game for the first time in his NHL career, and his third three-point game. ... Ruff needs one victory to pass Al Arbour (905) for the fifth-most wins by a coach in NHL history (regular season and Stanley Cup Playoffs combined).