Hunter slammed into the boards 40 seconds into the third and hit the edge after the door opened. He went down on his knees before rolling onto his back. A stretcher was brought out, but Hunter got to his feet and skated off toward the dressing room.
The Rangers turned the ensuing faceoff into Petr Prucha's second of the season nine seconds later. Michal Rozsival gave the Rangers their first lead with a sharp-angle goal at 2:08, but the Islanders needed only 27 seconds to tie it on Blake Comeau's second.
Naslund put the Rangers ahead for good at 7:12 with his team-leading 14th, snapping the team's longest losing streak of the season at three.
Prucha got back into the lineup after being benched for eight games and made the decision look good. His other goal this season came on Dec. 3, after he was benched for 10 games. Rozsival scored after missing one game because of a family illness.
Nigel Dawes made it 5-3 with 4:49 left, but Islanders got back within a goal when Mike Comrie scored with 18.7 seconds remaining - the sixth goal of the period.
Mike Sillinger and Kyle Okposo staked the Islanders to a pair of one-goal leads, but Joey MacDonald couldn't protect them.
A brief return by No. 1 goalie Rick DiPietro sparked the Islanders on Friday when they snapped a 10-game losing streak, and New York earned another point in a shootout loss at Buffalo on Saturday. DiPietro, who has played only four games this season, is sidelined again with a groin injury.
Sillinger gave the Islanders a 1-0 lead in the first period, and Okposo scored in the final seconds of the middle frame after Scott Gomez got the Rangers even.
The Rangers had held the Islanders to only 10 shots through the first 37 minutes. but couldn't get the lead.
Lundqvist kicked out a hard drive in the final minute of the second, but the puck never cleared the zone. A shot clipped Okposo's stick and bounded in with 11.7 seconds left.
The Islanders created a turnover down low and turned it into the first goal late in the first. Hunter shoved defenseman Dmitri Kalinin off the puck in the left corner, and found Sillinger open in front for a quick one-timer with 4:56 left.
Pleas for the Rangers to shoot the puck reached a crescendo midway through the second period when they held it in the Islanders zone for more than a half-minute during a delayed penalty. Brandon Dubinsky zipped a pass from the right circle down to Nikolai Zherdev at the left post - deftly sliding it under defenseman Freddy Meyer.
Zherdev saw Gomez cutting to the right post and hit him with a cross-crease feed for a tap-in at 8:29.
Notes: The Rangers held a 37-24 shots advantage. ... Islanders C Doug Weight returned to the lineup after missing three games due to a strained groin. ... Yann Danis was recalled from Bridgeport (AHL) to back up MacDonald. ... LW Aaron Voros, who played in the Rangers' first 38 games, was a healthy scratch. ... Islanders LW Andy Hilbert will miss two to four weeks due to a fractured foot.