Joe Pavelski had an assist in his 1,000th NHL game, and Tyler Seguin scored twice for the Stars (20-13-4), who have lost two of three since a five-game point streak (4-0-1).
"We've played a lot of good hockey for a long stretch," Pavelski said. "These last couple games, it's a good league. You probably get what you deserve most nights. ... Tonight, what we got was probably what we deserved. They're a good team. We weren't ready to go from puck drop, and we were exposed."
Acciari's first two goals came 32 seconds apart, giving Florida a 6-1 lead. He went five-hole on a one-timer, pushing the lead to 5-1 at 7:26 of the second period, before scoring on another one-timer at 7:58.
After being hooked by John Klingberg on a shorthanded breakaway, Acciari went five-hole on a penalty shot to make it 7-1 with his NHL career-high 11th goal at 11:25 of the second.
"He's like the best guy in the world, so to see him score back-to-back hat tricks, it couldn't happen to a better guy," Panthers forward Vincent Trocheck said. "It was a lot of fun watching him turn into Noel Gretzky out there, so hopefully it continues."
Seguin cut it to 7-2 on power play at 16:38 of the second before scoring again to make it 7-3 at 7:03 of the third. Jamie Benn scored for the 7-4 final with 6:58 remaining.
Dallas outshot Florida 15-9 in the second period, when it was outscored 5-1.
"It was good to see that we didn't quit, we did keep fighting," Stars coach Rick Bowness said. "I give the guys credit for that after being down by that score but again the opposition had a six-goal cushion. At least we didn't accept it either, we did fight back, so we hope that carries into Sunday."
Huberdeau, who had four assists against the Senators, opened the scoring on a power play for a 1-0 lead at 4:37 of the first period.
Denis Gurianov tied it 1-1 at 13:10 before Anton Stralman scored off Dallas forward Roope Hintz's skate, putting Florida ahead 2-1 at 14:48 of the first.
Trocheck made it 3-1 at 1:21 of the second, and Colton Sceviour scored from the left circle, extending the lead to 4-1 at 2:52.
Ben Bishop was pulled after allowing six goals on 20 shots for Dallas. Anton Khudobin made 12 saves in relief.
"When we play good defense it leads to offense, and I think that showed in the past two games but we can't stray away from that," Acciari said. "I think we got a little away from it in the third, and they kind of creeped back a little. We've just got to make sure we're playing a full 60 minutes and we're a tough team to beat."
