Palmieri deflected a shot from the slot 19:50 into the first to give the Devils a 1-0 lead. Florida used a coach's challenge for goaltender interference but the call on the ice was upheld.
"It was an offensive zone face-off," Palmieri said. "Hall did a good job winning the draw back to [Nico Hischier], who jumped in as a winger. I went to the net and set up in front of the net and was fortunate to get a lucky bounce after [Florida] carried the play in the first."
Palmieri has at least one point in seven of eight games this season and leads the Devils with 13 points (eight goals, five assists).
Hall made it 2-0 when he took a pass from Palmieri and scored 3:05 into the second. Hall's 11 points are his most through eight games in a season in his NHL career. Hischier had two assists and has six points (three goals, three assists) in his past four games.
"[Hall and Hischier] are two world-class players and they create space and set you up, and I think for me it's just about playing my game," Palmieri said. "That has resulted in some chances and they're going in for us right now. Let's hope it continues."
Coleman, who led the Devils with five hits, extended the lead to 3-0 when he deflected in a shot at 13:22.