Montoya, making his first appearance of the season, was busiest in the second period, turning aside all 11 shots he saw as the Jets grabbed a 1-0 lead on Evander Kane's shorthanded goal.
Kane later added an empty-netter and Andrew Ladd capped the scoring with 37 seconds left as the Jets rebounded from a 4-1 loss to Dallas Friday.
Cory Schneider made 32 saves for the Devils, who fell to 0-2-3 starting the season.
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