Zach Parise gave New York a 1-0 lead at 2:18 of the first period after Anaheim turned the puck over behind its net.
Gibson kept it a one-goal game with a save on Bailey off a 2-on-1 rush at 2:57, and he used his outstretched stick to keep a shot by Oliver Wahlstrom from crossing the line at 4:59.
Manson tied it 1-1 at 9:48, chipping in the rebound after Sorokin made a left pad save on Buddy Robinson's one-timer.
Sorokin made his best saves on back-to-back shots by Nicolas Deslauriers and Sam Carrick at 9:51 and 9:55 of the second period.
He also turned away Cam Fowler with his left pad twice in a row at 3:07 and 3:08 of the third.
"It wasn't our best performance on the homestead, but we got it done," Trotz said.
NOTES:Palmieri has scored eight points in his past eight games (four goals, four assists). ... Lee has scored seven goals in his past four games. .... Anaheim was without four of its top 12 forwards. Rickard Rakell sat out with an upper-body injury, Ryan Getzlaf (upper body) missed his fifth straight game, Jakob Silfverberg (lower body) his third straight, and Sam Steel (upper body) his second straight. ... Ducks rookie defenseman Jaime Drysdale returned after serving as a healthy scratch for the first time this season on Saturday and had an assist on Lundestrom's goal. ... Gibson is (2-8-0) in 10 starts since playing in the 2022 Honda NHL All-Star Game with an .840 save percentage. … The Ducks had gone 15 games without a goal by a defenseman until Manson scored in his second game back since missing 13 games with a finger injury. ... Ducks forward Trevor Zegras, who grew up about 45 miles north of Elmont in Bedford, N.Y., assisted on Henrique's goal. ... Anaheim forward Sonny Milano grew up 17 miles east of Elmont in Massapequa, N.Y. He was minus-1 in 16:44 of ice time. … Sorokin made 34 saves in a 4-0 win against the Ducks in Anaheim on Feb. 27.