United have won the storied under-18 tournament 11 times previously, a competition record, and were able to begin this season's campaign in triumphant fashion thanks to Gabriel's first-half goal.
Darren Fletcher's young side will now face either Cambridge United or Derby County at the next stage, with those teams due to meet in the third round on Wednesday.
FIRST HALF
Attacking the Stretford End in the opening 45 minutes, United nearly made the dream start. Right winger Bendito Mantato pounced on a heavy Peterborough touch and won the ball back inside the visitors' 18-yard area before squaring for Louie Bradbury, who was disappointed to roll his first-time right-footed effort wide.