The Texans tallied three goals in the third and Kari Lehtonen notched 35 saves to extend their winning streak to four games.
Eric Nystrom's scored his first goal of the season 44 seconds into the third to snap a 1-1 tie. Ryan Garbutt also scored in the third to close out the scoring.
Taylor Hall scored the Oilers only goal to open the scoring late in the first period. Devan Dubnyk allowed four goals on 29 shots for the Oilers, who have lost six of their last seven contests.
Brenden Dillon scored in the second period for the Stars to tie the score 1-1.