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.
"I thought our top guys weren’t very good tonight," Ducks coach Joel Quenneville said. "You could name them all and you probably wouldn't be happy.
"It was flattering, the score at the end of the night."
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.
"I've been on the other side when you're coming through this segue of teams here across the coast, it's tough," said Durzi, who previously played in Los Angeles, Arizona and Utah. "Knowing that now, being on this side, having that experience, starts are huge. I think starts all year have been pretty good for us all year, especially at home, and then it's staying on top of them."
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.
The Rangers have scored in the opening two minutes in three consecutive home games for the second time in team history. They also did it from March 15-22 in 1989.
"Disappointing more than anything," Quenneville said of Anaheim's slow start. "We didn't have much. When I say that, it's possession of the puck, play recognition, second battles or whatever. They played well, but we didn't really have anything that was dangerous to look like we had any chance of getting back in the game. That was (a) tough one."
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.
"That was an easy one," Perreault said.