Brenden Morrow scored one goal and assisted on two others, and Jeff Woywitka contributed one goal and an assist for the Stars, who pulled to within three points of Chicago for the eighth and final playoff spot with four games remaining.
Kari Lehtonen turned aside 24-of-27 shots and withstood a furious assault by the Ducks in the closing minutes.
Anaheim had two potential tying goals waved off in the final 2 minutes. Francois Beauchemin's tally was disallowed when Saku Koivu was ruled to have interfered with Lehtonen and Corey Perry's score with 48 seconds left came after a hand-pass.
Ryan Getzlaff and Lubomir Visnovsky scored and Perry added his league-leading 47th goal while shorthanded for the seventh-seeded Ducks.
Ray Emery made 27 saves for Anaheim.