The Devils (4-1-1) got on the scoreboard with less than a minute remaining in the first period, when Tuomo Ruutu deflected a shot from defenceman Adam Larsson past Rangers goalie Cam Talbot.
The 42-year-old Jagr, beginning his second season with New Jersey, made it 2-0 at 7:20 of the second period when he took a rebound of a shot by Larsson and put a pretty backhand past Talbot.
Dainius Zubrus capped the scoring on a deflection with less than 12 minutes left.
Talbot finished with 21 saves for the Rangers (3-3-0).
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