Michael Tellqvist made 29 saves for his third career shutout and first for the Coyotes, who won for just the second time in seven games (2-4-1).
The Ducks, winners of 12 of their last 14 overall, had won 10 of their last 11 against Phoenix. Anaheim was shut out for the second time this season.
Mike Comrie fired a long shot from just inside the blue-line which goalie Jean-Sebastian Giguere kicked onto Doan's stick just inside the right faceoff circle. Doan then fired the rebound into the open right side of the net for a 1-0 lead with 5:02 to play.
Ballard made it 2-0 when he one-timed a long pass from Owen Nolan past Giguere from the point.