Reimer's shutout was his third of the season for Toronto, which strengthened its grip on the No. 5 in the Eastern Conference seed after notching at least one point in 13 of its last 14 games.
Phil Kessel's power-play goal with 6:32 left in regulation broke a scoreless tie and Jay McClement added an empty-netter.
Martin Brodeur needed to stop only 12 shots but yielded the decisive tally late as the Devils tumbled to a club record-tying 10th straight loss.
Last year's Stanley Cup runner-ups fell six points behind the eighth-seeded New York Rangers with six games to play.
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