Steve Ott, Fabian Brunnstrom, Brad Richards, Krystofer Barch and Mike Ribeiro also scored for the Stars (14-14-5). Jere Lehtinen, Landon Wilson, Trevor Daley and Stephane Robidas added two assists each.
Jason Blake and Mikhail Grabovski scored for Toronto (14-14-6).
It didn't take long for the Stars to look dominant -- they were up 3-0 before the Leafs had a shot on goal. Neal, Ott and Brunnstrom scored on Vesa Toskala in the first 10:45 of the game.
Playing for the fourth time in six nights, the Leafs looked sluggish in the defensive zone. Dallas was having its way, showing as much speed as any visiting team has all season and moving the puck with authority.
The sellout crowd of 19,269 started getting on Toskala after he allowed a power-play goal to Richards at 14:12 of the first period. Toronto's starting goalie missed Monday's win in Atlanta while receiving treatment for a groin injury.
Toronto repeatedly was burned for leaving Stars players uncovered in front of the net.
Barch was left unchecked during a prolonged goal-mouth scramble, eventually scoring from his knees to make it 5-0 at 3:45 of the second period.
Then Ribeiro was barely touched at the edge of the crease as he calmly shoveled the puck into an open net at 10:15. And Neal's second of the night came after another scramble at 11:35.
It was 7-0 by the time Maple Leafs coach Ron Wilson gave Toskala a break and sent Curtis Joseph in to replace him.
The Maple Leafs had won five of six coming in and hadn't shown a propensity for embarrassing defeats as did the team of year ago, when Toronto lost five games on home ice by five or more goals.
Marty Turco lost his shutout bid when Blake took a pass from behind the net and scored at 15:33 of the second period.
Grabovski added a goal at 9:20 of the third before Neal polished off a hat trick at 18:34 in a nearly empty building. Those that stayed around booed the home team as the seconds ticked away.
Notes: @Dallas played at Toronto for the first time since Dec. 10, 2005. ... Turco has a record of 48-13-4 against Canadian teams since 2002-03 ... The Stars and Leafs are both looking for their first short-handed goal this season ... Andre Deveaux earned his first NHL point with an assist on Toronto's second goal.