Neal took a shot from the middle of the right circle that went over the shoulder of goalie Nikolai Khabibulin and ricocheted out of the net so quickly that play continued until the whistle blew for an apparent penalty. Officials then looked at a video replay and awarded the goal.
Neal's 16th of the season, with 11:09 left, came soon after the Oilers scored twice in less than 2 minutes to tie the game. Kari Lehtonen stopped the other 39 shots by Edmonton, which has won only one of its last 10 games (1-7-2).
Jamie Benn scored his third goal in two games for Dallas and captain Brenden Morrow also scored.
Jamie Langenbrunner, reacquired last week from New Jersey, played his first home game for the Stars in nearly nine years. The right wing was scoreless, but the crowd cheered loudly when he got in a fight late in the second period.
Edmonton finally scored on its 27th shot, with 14:10 left, when Jean-Francois Jacques flicked a rebound up and over Lehtonen's glove for his second goal of the season. On another rebound that the Stars failed to clear, Ryan Jones got his 10th goal of the season with 12:22 left.
The Pacific Division-leading Stars had been 0-3-2 at home since a win over Montreal on Dec. 21. In that same span, they have set a franchise record with a seven-game road winning streak, including a 4-0 win Sunday at Minnesota when Benn scored twice.
Benn's goal Tuesday, his 12th of the season, came in the second period when he passed the puck to Steve Ott to his left. Ott then twisted his body and passed back to Benn, who knocked it in for a 2-0 lead.
Morrow got his 18th goal, matching All-Star center Brad Richards for the team lead, on a one-timer from Mike Ribeiro with 5:28 left in the first period.
Last-place New Jersey traded the 35-year-old Langenbrunner, its captain, to Dallas on Friday. Langenbrunner was drafted by the Stars in 1993 and was part of their only Stanley Cup championship in 1999, then another Western Conference title the following season. He was traded to New Jersey in 2002 and was on the Devils' Stanley Cup-winning team in 2003.
Langenbrunner appeared on the ice for the first time about a minute into the game, getting a nice ovation. That turned into a loud cheer late in the second period when he and Kurtis Foster got tangled up and wrestled, though both got 5-minute fighting penalties.
In the third period, Langenbrunner and Ladislav Smid both got 2-minute roughing penalties after a scuffle.
Both teams had apparent goals wiped out in the second because of interference against the goalies.
With about 13½ minutes left in the period, Foster knocked a puck in from the right circle, but officials quickly disallowed the goal because Linus Omark made contact in the crease with Lehtonen.
About 11 minutes later, Ott thought he had scored but officials ruled Adam Burish interfered with Khabibulin, who made 17 saves.
NOTES: Edmonton has not won in regulation at Dallas since Dec. 8, 2006. The Stars are 7-0-1 against the Oilers at home since then. ... The Stars and Oilers played for the first time this season. They play four times in all, three of those games this month. ... Dallas assigned RW Brandon Segal to the Texas Stars of the AHL after he cleared waivers Tuesday. He had been placed on waivers to make room on the roster for Langenbrunner.