The Pacific Division-leading Stars have a 14-7-1 road record this season and they recorded their fifth straight victory overall. Dallas has lost just once in 2011 and that setback came in overtime.
Kari Lehtonen made 30 saves to get the victory.
Mike Ribeiro gave Dallas the lead for good at 2-1 early in the second period and Neal expanded the advantage on the power play with 7:09 to go in the middle stanza.
Jeff Petry brought the Oilers within one by scoring his first NHL goal with 1:08 remaining in the second. Petry was playing in his 11th game with the Oilers.
Lehtonen protected the narrow advantage the rest of the way and Dallas tacked on a goal in the final second when Adam Burish scored into an empty net.
Edmonton has lost four in a row and is 2-11-2 in its last 15 games. Nikolai Khabibulin allowed three goals on 23 shots.