Jose Theodore was the tough-luck loser, giving up one goal on 26 shots for the Panthers, who dropped their third straight.
Anaheim opened the scoring at 12:13 of the first period.
Saku Koivu, shielding the puck along the left wall, dished to Bobby Ryan in the left circle. Ryan fired a quick wrister on net that was kicked out by the left pad of Theodore, but Selanne was parked in front and slipped it under the arm of Theodore for a 1-0 Anaheim lead.
With the goal, his 20th of the season, Selanne has 657 goals for his career, which puts him one ahead of Brendan Shanahan for sole possession of 12th place on the NHL's all-time goal scoring list. He is four goals shy of the Philadelphia Flyers Jaromir Jagr for 11th place (661).
"Everybody has the belief that we can climb back (into the playoffs)," Selanne said. "We're still not really there, but it's good to get a win tonight. I don't think we played that well, but Jonas was really good today."
Florida elected to pull Theodore following an icing call with a minute to go and got some good shots on net, but Hagman put the game away when he found the empty net with 14.3 seconds left.
Hiller made 11 stops in the third period to preserve the shutout.
"We certainly need to find ways to score goals," Panthers head coach Kevin Dineen said. "Right now we're not creating enough on the offensive end to get us two points at the end of the night."
The Panthers have lost five of their last six games against Anaheim, and have not beaten the Ducks on home ice since a 3-2 victory on December 27, 2003...Perry had his four-game goal scoring streak snapped...Anaheim failed to convert on two power-play chances, while the Panthers failed on four tries with the man-advantage...Florida will host the Minnesota Wild on Thursday, while the Ducks will visit the Tampa Bay Lightning on Tuesday.