Scott Gomez and Markus Naslund each tallied a goal for the Rangers, who have won their last two after a four-game losing streak. Henrik Lundqvist made 28 saves in the win.
The Rangers, Florida and Pittsburgh all have 74 points to occupy the final three spots in the Eastern Conference playoff hunt.
The Rangers had three new faces on the team as Sean Avery, Nik Antropov and Derek Morris all put on the Blueshirt jersey for the first time this season.
"It was such a close game, I was just trying to concentrate on making good plays and getting used to my linemates," Avery said. "
The Rangers claimed Avery off re-entry waivers from the Dallas Stars on Tuesday. The Stars had placed the embattled forward on re-entry waivers Monday, after Avery had not suited up for the club since his inappropriate comments in Calgary on December 2 eventually led to a league-imposed six-game suspension.
Avery had been playing for the Rangers' American Hockey League affiliate in Hartford since Dallas placed him on regular waivers on February 7 and assigned him to the club three days later. Dallas does not have its own AHL affiliate.
The 28-year-old had played for the Rangers from 2006-08, scoring 23 goals with 53 points and racking up 212 penalty minutes. However, he left Broadway this summer to a sign a four-year, $15.5 million deal with the Stars.
"When he focuses on the game, he's a good player," Lundqvist said of Avery. "He has a lot of speed and he can shoot the puck. There's a lot of attention on him right now and I think he did a good job to keep cool and play his game."
Antropov, who had 21 goals and 25 assists in 63 contests with the Leafs this season, was picked up for a second-round draft pick and a conditional draft pick at Wednesday's trade deadline. For Morris, also a deadline deal, the Rangers had to give up defenseman Dmitri Kalinin and forwards Petr Prucha and Nigel Dawes. Morris had five goals and seven assists in 57 games with Phoenix this year.
Blake Comeau had a goal and an assist for the Islanders, who had a two-game winning streak stopped. Yann Danis stopped 19 shots in the loss.
The Islanders made just one move at the deadline as they sent veteran winger Bill Guerin to Pittsburgh for a conditional draft pick.
The Rangers took a 1-0 lead just 8:33 into the game. Tim Jackman grabbed the puck in the Islanders' end and from the right boards attempted to clear the puck out with a backhand. However, Zherdev intercepted the attempt, skated to the right circle and snapped a shot past Danis.
Lundqvist was perfect in the first period as he stopped all 10 shots he saw.
The Islanders tied the game at the 5:37 mark of the second period. Dean McAmmond charged the net from the left wing and shot the puck on net. Lundqvist stopped the shot, but Comeau followed up and stuffed the puck underneath the goaltender.
However, the Rangers took a 2-1 lead with a power-play goal as Drury blasted a slap shot from the high slot through a screen and past Danis at the 9:41 mark of the second.
The Rangers made it a 3-1 game just 49 seconds into the third. An Islander turnover in the Rangers' end resulted in a 2-on-1 the other way. Zherdev skated down the right side and dished it over to Gomez on the left for the easy slam dunk.
The Islanders made it a one-goal game less than three minutes later. Jack Hillen charged through the neutral zone and as he gained the Rangers end left a drop pass for Comeau. With Hillen continuing to move forward, Comeau dished it down low for Hillen, who charged the net and stuffed it past Lundqvist for his first NHL goal.
The Rangers, though, sealed the win with 6:36 to play with another power-play tally as Naslund blasted a shot from the right point that hit off an Islander and floated into the net.