Scott Gomez had a goal and one assist for the Rangers, who scored five goals in regulation for only the third time all season. Michal Rozsival, Petr Prucha and Markus Naslund also scored for the Rangers, while Henrik Lundqvist earned the win with 20 saves.
Mike Comrie had a goal and an assist for the Islanders, who have dropped 12 of their last 13 games. Mike Sillinger, Kyle Okposo and Blake Comeau added goals and Joey McDonald took the loss despite 32 stops.
Prucha scored just his second goal of the season 49 seconds into the third period and Rozsival gave the Blueshirts a one-goal lead at 2:08. Comeau brought the Islanders back on a rebound 27 seconds later, but Naslund tipped in a Gomez feed at 7:12 for a 4-3 Rangers advantage.
Dawes provided a two-goal cushion with 4:49 to play.