New Jersey lost for only the second time in nine games and remained six points behind Buffalo in the scramble for the final playoff berth in the Eastern Conference.
Ryan Shannon gave Ottawa a 1-0 lead with 58 seconds left in the opening period and there was no further scoring until Neil put a slap shot past Martin Brodeur 55 seconds into the third.
Brian Rolston brought the Devils within one 5 minutes later but Neil clinched the win by scoring into an empty net with 38 seconds to play. The goals were Neil's fourth and fifth of the season.
Brodeur allowed two goals on 24 shots.
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