The Eagles had the ball with a final chance to erase a seven-point deficit when Allen picked off a pass thrown by Matt Barkley.
That gave New York a 27-13 lead and allowed the Jets room to survive a 1-yard touchdown run by the Eagles' Matthew Tucker with 35 seconds remaining.
Matt Simms, listed as the No. 4 quarterback on the New York roster, played the entire game and completed 33-of-44 passes for 285 yards without a touchdown or interception.
Kahill Bell ran for two New York scores on carries of 8 and 2 yards. He gained 80 yards on 21 carries.
Nick Foles and Barkley shared time at quarterback for the Eagles and combined to complete 19-of-44 passes for 197 yards.
The Jets finished the exhibition season at 3-1 while the Eagles were 2-2.
New York will get its regular season underway with a home game on Sept. 8 against Tampa Bay. Philadelphia will open one night later at Washington in the first of the two Monday night tilts.