Hylton, signed from non-league Redditch United in January, replaced Andy Williams, who crashed a hotly-disputed first-half penalty against the crossbar.
It was the 21-year-old’s maiden league goal and at the very least it cemented the Robins’ spot in the play-offs.
Hylton emerged from the bench in the 68th minute and scored almost immediately – Jon Obika teeing up the chance after neat approach play by John Swift and Harry Toffolo.
Without a goal in four games, Peterborough will consider themselves unlucky to have suffered a third defeat either side of Easter.
Posh had a good shape and worked hard, but their efforts in the final third let them down.
Marcus Maddison missed a good chance two minutes into the second half, while caretaker manager Dave Robertson was unhappy that referee Andy Davies turned down a late penalty appeal when Conor Washington appeared to have been pushed over.