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.
The Coyotes' Mike Zigomanis tied it at 2:07 of the third period. Georges Laraque, whose goal late in the second period pulled Phoenix within 4-3, set up Zigomanis' third of the season with a pass from the boards behind the goal line on the right side.
Laraque got his fourth goal of the season when he deflected Jovanovski's long shot in at 19:24 of the second period.
After the Coyotes' Yanic Perreault scored on a power play at 11:56 of the second to trim Anaheim's lead to 3-2, Kunitz quickly built the Ducks' lead back to two. Kunitz beat Joseph between the pads at 12:57 of the period.
Selanne made a fine play to set up Kunitz's goal that gave Anaheim a 3-1 pad early in the second period. Weaving his way through a couple of defenders as he skated toward the crease from near the goal line on the right side, Selanne waited until Joseph had to commit to that side, then slid the puck across the crease.
Kunitz was there to knock it in.
Jovanovski gave Phoenix a quick lead with his power-play goal at 3:09, but McDonald evened it on a power play at 7:53.
Jovanovski scored his fourth goal on a 50-foot slap shot.
Notes: Selanne's five assists tied the club record set by Dmitri Mironov on Dec. 12, 1997, against Washington. The five-point game was the seventh of Selanne's career. ... Anaheim is 13-0-1 against the Coyotes since Nov. 9, 2003. ... McDonald's two-goal game was the eighth of his career and first this season.