"We talked after the second of just continuing to play our game," Ducks coach Bruce Boudreau said. "We were very calm about it and knew if we got one quickly, we'd have a great chance."
Down 3-1, the Ducks scored four times in the third period. The Islanders played a spirited first two periods, taking their lead on two goals by Thomas Vanek and another by Frans Nielsen.
But Getzlaf scored his second of the game at 1:10 of the final period and Mathieu Perreault tied it at 10:32.
Kyle Palmieri, a native of Montvale, N.J., who scored the overtime winner Friday night against the New Jersey Devils, found himself in front of Evgeni Nabokov with a clear shot at 13:44. The 22-year-old forward, who also scored the winning goal when the Ducks beat the Rangers 2-1 at Madison Square Garden on Nov. 4, knocked in his sixth goal of the season.
"Those goals feel really, really good," Palmieri said. "We find ways to win and tonight was another example of our patience and skill."
Getzlaf completed his hat trick with an empty-net goal. The Ducks won in their first visit to Long Island since a 3-2 loss on Dec. 16, 2010.
"We didn't move the puck the way we should have in the third period," Islanders coach Jack Capuano said. "You can't play the way we played in the third period against a big Stanley Cup-caliber team like this. It won't work."
Vanek finally had the type of game the Islanders envisioned when they acquired him from Buffalo for popular left wing Matt Moulson on Oct. 27.
The Austrian right wing opened the scoring at 11:27 of the first, putting a rebound past backup goaltender Frederik Andersen, who made 18 saves to improve to 9-1.
After Getzlaf tied the game at 15:10 of the second, Vanek gave the Islanders again with a perfectly placed shot as he sped down the right side, beating Andersen to his stick side at 17:55.
The goal was Vanek's ninth since joining the Islanders and his third in two nights. Nielsen made it 3-1 for the Islanders 57 seconds later.
"It came down to execution," Capuano said. "We were icing the puck too much and not making plays when we had to in the third period."
Anaheim forward Teemu Selanne was a healthy scratch. The 43-year-old Selanne usually doesn't play the second half of back-to-back games. Selanne played Friday night as the Ducks upended the Devils 3-2 in overtime.
This was the 10th time in 36 games this season the Islanders have lost a third-period lead. ... The Ducks will complete their final Eastern trip of the season at Washington on Monday. ... Forward Dustin Penner and defenseman Hampus Lindholm were healthy scratches for the Ducks, as were Islanders forwards Colin McDonald and Peter Regin, plus defenseman Aaron Ness. ... Anaheim also continued to be without goaltender Viktor Fasth (lower body) and defensemen Luca Sbisa (hand) and Sheldon Souray (wrist). ... The Islanders have been without defenseman Lubomir Visnovsky (concussion) since has injured Oct. 19.
Copyright by STATS LLC and The Associated Press
UNIONDALE, NY - DECEMBER 21: Cal Clutterbuck #15 of the New York Islanders checks Kyle Palmieri #21 of the Anaheim...