The victory ended the Coyotes' 10-game losing streak against the Ducks in Anaheim dating to the 2003-2004 season. They also beat Anaheim goalie Ilya Bryzgalov for just the second time in his nine games against them.
Weller, a 26-year-old signed as a free agent in July, scored the game's lone goal early in the second period.
Auld, who also signed as a free agent over the summer, made Weller's goal hold up. He stopped 31 shots, many of them with heavy traffic in front of him.
The 26-year-old Auld spent last season with Florida, where he went 7-13-0-5 in 27 appearances. He was with Vancouver the previous season, going 33-26-0-6 in 67 games.
A rangy six-foot-five, 221-pounder, Auld evened his record with the Coyotes to 2-2.
Niko Kapanen set up Weller's score. Kapanen skated down the slot, slid a pass out to Weller on the right wing and Weller snapped off a shot that beat Bryzgalov high on the glove side at 3:02 of the second.
Weller, a sixth-round pick by St. Louis in the 2000 entry draft, played at Hartford of the AHL for the past four seasons and was the team captain last year.