The Islanders thought they tied the game at 6:24 of the second period when Mathew Barzal poked the puck across the goal line after Gibson covered it with his glove, but the NHL Situation Room concluded Islanders forward Cal Clutterbuck interfered.
"That's a big momentum swing," Barzal said. "That happens. Just can't control it. Got to get back on the horse quickly."
Kesler then made it 2-0 at 8:20 of the second period on a long wrist shot that beat Greiss stick side.
It was Kesler's first multigoal game since his hat trick in a 4-3 shootout win against the Philadelphia Flyers on Jan. 1, 2017.
Kesler, 34, sat out the preseason and first three games to gain strength and conditioning after having hip surgery in June 2017. He has four points (three goals, one assist) in four games.
"I think I have a lot to improve on," Kesler said. "It's a long year, but it's a good start. I'm just trying to help my team win out there."
Henrique scored his third goal of the season 42 seconds into the third period. Ducks rookie forward Max Comtois drove to the net and Greiss made the initial save, but the puck caromed in the air and Henrique knocked it out of mid-air to make it 3-0.
The Islanders went on their final power play at 16:21 of the third period and pulled Greiss for a 6-on-4 advantage, but Gibson made four saves. He made 13 of his saves on the penalty kill.
"I thought our line had some good looks," Barzal said. "I thought everybody actually got involved. D-men were trying to get (shots) through, but just a couple inches on a couple goals, a couple plays and it's a different game. I don't think we are too worried with the way we played tonight. I liked our effort."
New York was 0-for-4 on the power play; Anaheim was 1-for-3.
"Historically, special teams have been a real determining factor early in the season more so than later in the season," Ducks coach Randy Carlyle said. "If you can have an effective penalty kill, it gives you a chance to get points in every game. You can sometimes survive without an effective power play, but tonight we were able to find the back of the net and prevent the Islanders from scoring on their power play."