The last of Kunitz's three goals broke a 4-4 tie and came on a deflection at 9:21 of the third period, off a 45-foot shot by Selanne. Phoenix goalie Curtis Joseph almost blocked the puck, but it trickled past him and across the line to give Kunitz his 13th goal of the season.
Rob Niedermayer added an empty-net goal with 2.8 seconds left, his second score of the season.
Andy McDonald had two goals and two assists for the Ducks, who defeated the Coyotes for the third time this season and eighth in a row overall.
Ed Jovanovski had a goal and two assists for Phoenix.
Anaheim got off 30 shots at Joseph, while the Coyotes recorded 28 on Jean-Sebastien Giguere.