Argyle's youngsters maintained their unbeaten start to life in the Merit League One after a third victory in their four opening four games.
Northern Ireland under-19 International striker Louis Rooney continued his run of scoring with two more goals taking his tally to 18 for the season.
Yet it was the Hatters who opened the scoring when Argyle lost possession allowing the home side to break away and score on 24 minutes.
Argyle required just two minutes to restore parity as a free kick into the home area found Rooney reacting the fastest to lash the ball into the roof of the home net.
The visitors took the lead two minutes before the break when Ben Steer burst into the Luton area only to be blatantly fouled. Rooney to coolly converted the penalty to Argyle a lead they would not relinquish.
Argyle should have really scored more goals in the second half but in the end will be satisfied with yet another victory.
Argyle: Cory Harvey, Mason Hughes, Owen Jones, Will Sargent, Tom Moxham (Liam Knowles 80), Billy Palfrey, Jack Calver (Jamil Roberts 70), Callum Hall, Ben Steer (Dan Rooney 80), Louis Rooney, Jason Vincent.