Prucha smacked in a shot from the slot, off a feed from Michael Nylander with 5:14 left in the game and 1:17 into Simon's penalty. Simon was ejected after he flattened Rangers forward Ryan Hollweg by clotheslining him with his stick.
The Islanders killed off the rest of the power play and thought they tied the game with 20.4 seconds left. Marc-Andre Bergeron's shot was stopped by Henrik Lundqvist and Trent Hunter slid the puck back to the goal line where Lundqvist barely swept it out.
After a lengthy video review, with fans chanting "Goal, goal," while accompanied by the organist, referee Kevin Pollack signalled no goal.
It was the second crucial call to go against the home team during an action-packed third period.
Hollweg drove Simon into the boards with a hard, clean check. Simon got up angrily and met Hollweg as they came together again. Hollweg fell to his back and rolled over onto his stomach by the boards. He was motionless for a few moments, and was bleeding from his chin when he got up.
Simon, who gave the Islanders a 1-0 lead in the second period, was ejected - slapped with a match penalty for deliberate attempt to injure.
Paul Mara scored a power-play goal for the Rangers to tie it in the middle period. The Rangers used a pair of 2-1 wins over their biggest rival to move into position for the final playoff spot in the Eastern Conference.