The Rangers (7-3-1) have won six consecutive home games (6-0-0) to start the season for the first time since 1990-91, when they won their first eight games at the Garden. They didn't win their sixth home game last season until Jan. 26.
Oliver Bjorkstrand scored two goals, Sean Durzi, J.T. Miller and Gabe Perreault each had one, and Alexis Lafreniere had two assists for New York.
Dylan Garand made 29 saves for the Rangers. He has allowed two or fewer goals in five of six starts this season and eight of nine in his NHL career.
Anaheim (4-4-0) lost its third straight game since winning four of five to start the season. Nick Jensen and A.J. Greer scored 36 seconds apart late in the third period, and Ville Husso made 25 saves for the Ducks.
The Ducks were delayed getting to New York on Sunday because of plane maintenance that led to a 15-hour travel day with a three-hour time difference thrown into the mix. They didn't arrive at their hotel until 2:30 a.m. Monday.
The Rangers jumped on their road-weary opponent early with Durzi scoring with a snap shot from the point through traffic at 1:18 of the first period to give New York a 1-0 lead.
Miller extended the lead to 2-0 with a power-play goal at 4:38 of the second period. He set up in front and deflected Adam Fox's wrist shot from the point.
Perreault made it 3-0 at 10:17, finishing a tic-tac-toe passing sequence that started with Durzi's forecheck down the right-wing wall. Lafreniere supported Durzi from behind, got the puck and went around Ducks forward Beckett Sennecke before whipping a backhand pass from the right circle to Mika Zibanejad in the left circle. Zibanejad one-touched a pass to Perreault at the right post, who settled the puck and scored.
Bjorkstrand made it 4-0 less than three minutes later when he intercepted Sennecke's backhand pass into the middle of the Ducks' defensive zone, went in alone on Husso and scored at 13:14.
Bjorkstrand tallied again, this time with a snap shot through the legs of Husso off a pass from Taylor Raddysh, to make it 5-0 at 3:26 of the third period.
Jensen broke Garand's shutout bid at 18:51 to make it 5-1 with a slap shot over Garand's stick from the slot, and Greer was credited with a goal that went in off the goaltender at 19:27 for the 5-2 final.
