"It gives our guys a little bit of confidence that we can play with some of the top teams record-wise in the East," Islanders coach Jack Capuano said of the streak, which also features wins against the Pittsburgh Penguins and Washington Capitals. "They're a good team and their record says that they are."
WATCH: All Rangers vs. Islanders highlights
Jimmy Vesey and Marc Staal scored for the Rangers (17-9-1), who were 0-for-6 on the power play and lost forwards Matt Puempel (concussion) and Rick Nash (groin) to injury. Henrik Lundqvist made 28 saves.
Mayfield, who was recalled from Bridgeport of the American Hockey League earlier in the day, gave the Islanders a 1-0 lead when he beat Lundqvist with a slap shot at 7:03 of the first period.
Chimera made it 2-0 with his third goal in the past four games at 17:24, redirecting Brock Nelson's shot past Lundqvist shortly after Nelson finished serving a four-minute high sticking penalty.
"We had some real good looks in the first period on our power play; their goaltender made some big saves," Rangers coach Alain Vigneault said. "You've got to score those timely goals, and we didn't do it tonight. We had the looks.
"I thought we battled hard. We tried to come back, but their goalie without a doubt was the best player on the ice tonight and we didn't finish on our opportunities."
Vesey scored 56 seconds into the second period when he put Nash's rebound past Halak to make it 2-1, but the Islanders responded when Ladd collected Shane Prince's rebound in the slot and put scored at 2:18.
Staal made it 3-2 when he took a pass from J.T. Miller and beat Halak with a shot from the right circle at 8:54.
Tavares sealed it with a power-play goal at 11:13 of the third period, beating Lundqvist with a wrist shot from the right circle.
"It's a long season," Tavares said. "We've certainly had some ups and downs and some frustration to start the year, some results we didn't get and some things maybe not go our way, (but) we're certainly playing a lot better hockey and we know we can still be a lot better. That's really the mindset."
Nash left the game in the second period because of a lower-body injury. Puempel was injured in the first on Nelson's high stick.