The Ducks (3-1-1), who took a 3-0 lead on Adam Henrique's power-play goal at 8:09 of the second, failed to match the best five-game start in their history. They went 3-0-2 on the way to a 12-0-4 start in 2006-07, when they won the Stanley Cup.
Anton Khudobin made 22 saves in his first start for the Stars, who signed him as a free agent July 1.
Anaheim goalie John Gibson made 40 saves on 44 shots through the second period. He was replaced at the start of the third by Ryan Miller, who made six saves.
"We hung our goaltender out to dry," Ducks coach Randy Carlyle said of Gibson, who didn't allow more than two goals in his four previous games. "That's inexcusable for a hockey club to play and rely on and put a guy in that type of situation, under siege for 20 minutes. It started with the very first shift. They pushed their game up. They pushed the walls, and then we didn't win enough battles."