Substitute Rhys Shirley's equaliser, in the third minute of stoppage time, ended the young Pilgrims’ run of three consecutive defeats Youth Alliance defeats.
Argyle opened the scoring on the half hour, when Angel Waruih's corner found Finley Craske, who headed the ball on for Ethan Mitchell to apply the finishing touch.
The young Pilgrims held that lead until the 70th minute, when Zeph Collins shot home when the Greens' defence failed to clear their lines.
Zeph’s twin brother Eli Collins then broke clear, with the Argyle defence appealing in vain for offside, to shoot across goalkeeper Tyler Coombes and inside the far post to hand the Grecians the lead.
Argyle surged forward in search of a response, and were rewarded deep into stoppage time, after Waruih and Will Jenkins-Davies combined down the left for Shirley to volley home the latter's cross from six yards.
Under-18 coach Darren Way was delighted with the character of the display, as well as large parts of the performance: "We controlled the game for long periods, playing the ‘Argyle way’ which was good, as you could see we had an identity in what we are trying to create at the football club.
"This will always take time, but to witness that against a strong Exeter team was really pleasing for the staff and players.
"We were disappointed with the two goals. The lack of discipline from the set play and then not securing possession in the final third cost us dearly.
"Other than that, the players showed a real desire and commitment to win the game, and we are getting closer to achieving our aims."
Argyle: Tyler Coombes, Oscar Rutherford, Finley Craske, Ethan Mitchell, Brandon Pursall, Carlo Garside, Angel Waruih, Jeremiah Medine (Charlie Miller 85), Will Jenkins-Davies, Oscar Massey (Rhys Shirley 70), Scott Crocker (Jamal Salawu 85). Substitutes not used: Lewis Moyle, Ali Mansaray.