The win ended a skid of six consecutive losses in regulation for the Stars, a level of futility not seen since December 1995.
Ryan Garbutt scored a goal and had two assists for Dallas. The Stars also had a goal from Erik Cole and a goal and an assist apiece from Trevor Daley, Jamie Benn and Cody Eakin. Benn's power-play score at 10:22 of the first period proved to be the deciding goal.
Edmonton saw its fortunes continue to sink. The Oilers lost their seventh in nine games.
Justin Schultz scored for Edmonton at 3:40 of the first period to tie the score 1-1. Sam Gagner added a power-play goal in the second to cut the Dallas lead to 4-2. Ilya Bryzgalov allowed four goals on 29 shots.
Edmonton was 1-for-2 on the power play and Dallas scored on its only power play.