Brock Nelson and John Tavares scored in regulation, and Josh Bailey recorded the overtime winner that gave the Islanders their first win of the season (1-2-0, 2 points).
Despite the loss, Getzlaf said he was pleased with the resiliency his club showed following a shakey opening frame that saw the Islanders out-shoot the Ducks, 16-3.
"I thought we put that first period behind us and got going after that," Getzlaf said. "We played a pretty solid game. We gave up that one goal, but we were able to get a point and that's big for us to keep building."
New York struck first when a failed clearing attempt by Anaheim allowed the Islanders to keep position down low, where Jason Chimera floated a pass into the slot and into the feet of Getzlaf. The puck took a fortunate bounce onto the tape of Nelson, who, in one motion, spun his body to sling it past Gibson to give the Islanders a 1-0 lead.
Nelson, who tallied 26 goals and 40 points last season, has recorded points in three consecutive games to start the new season (2g/1a).
The Ducks have yet to play with a lead at any point during their three games thus far. Getzlaf says he and his teammates will have to look back upon early-season struggles last season to find answers this time around.
"Our first period wasn't good tonight, but I thought we've played great in the first period in the past two games," he said. "We just weren't getting those bounces where we're used to getting goals. We have to look upon last year where we struggled scoring. We'll tighten things up defensively and get things done."
The Islanders nearly took a 2-0 lead midway through the second period when Anders Lee's deflection on a 2-on-1 caromed off the right post and trickled across the goal line.
Anaheim's best scoring chances came on a power play near the end of the middle frame after Cal Clutterbuck was whistled for tripping at the 16:30 mark. The Ducks, who were outshot 16-3 after 20, were the ones who dictated the pace in the second period, outshooting the Isles 13-5.
New York's lead grew to 2-0 after Tavares gathered his own rebound and buried it past Gibson. The goal was reviewed, however, after Clutterbuck appeared to play the puck with a broken stick before dishing it to Tavares.
But less than a minute later, the Ducks would get one back. After corralling a pass at the left point, Fowler sent a wrist shot on net that deflected off an Isles defenseman and past Halak to cut the deficit in half. The goal was Fowler's second of the season and second in as many games.
And with a minute remaining in regulation, the captain delivered. After pulling Gibson for an extra attacker, the Ducks tied the game on a great sequence that saw Fowler shovel a pass over to Vatanen, who quickly went cross-ice to Getzlaf, who hammered a one-timer from the left dot that beat Halak shortside.
Overtime was short-lived, however, as Bailey was able to walk around Corey Perry and Andrew Cogliano before out-waiting Gibson to seal the victory for the Islanders.
Despite the point earned, the Ducks fell to 0-2-1 on their season-opening five-game road trip that continues on Tuesday in New Jersey and Thursday in Philadelphia.
