Anaheim won for just the third time in 14 games. With nine victories for the season, the Ducks are tied for fewest in the NHL with Carolina, Columbus and the New York Islanders.
Pelley was obtained in a trade this week with New Jersey, where he had spent four full seasons and part of a fifth. He scored with 4:12 left in the first period to put the Ducks in front, producing his eighth goal in 212 career games.
Hagman tallied twice in the second period, one of the goals coming on the power play, giving Anaheim a 3-1 lead at the end of the stanza.
The Ducks got a goal in the third from Kyle Palmieri, who was playing in just his second game of the season and the 12th of his career. It was his second NHL goal.
Jonas Hiller made 19 saves to get the win. It was only his third in 12 appearances.
All four Anaheim goals came against Mike Smith, who stopped 24 shots. Phoenix has dropped three in a row.