In a result that defied recent form, the young Pilgrims suffered their first defeat in the month of October on the road against Cheltenham Town.
In scintillating form heading into the game, the Greens got off to the perfect start through Will Jenkins-Davies, who latched onto Scott Crocker's cross to fire home from 10 yards.
The lead only lasted seven minutes, though, as the Robins capitalised on a misdirected back-pass to put a striker in on goal to fire past the exposed Tyler Coombes.
Argyle restored their lead on 20 minutes as Rhys Shirley's pace and trickery won a spot-kick, which he picked himself up to convert for his seventh goal of the season.
The second-half was 10 minutes old when the Argyle defence was caught napping to allow the home side to level the scores, before a home striker worked his way free in the box to tap the Robins into a 70th minute lead.
Argyle came back to equalise eight minutes from time, as wing-back Oscar Rutherford made one of his trademark runs down the right. His cross was flicked on by substitute Oscar Massey for Jamal Salawu to slot home.
Unfortunately, parity did not last long, as Cheltenham netted the seventh, and final, goal of the match to record a surprise victory.
Plymouth Argyle: Tyler Coombes, Oscar Rutherford, Brandon Pursall, Oscar Halls (Charlie Miller 50), Ethan Mitchell, Jeremiah Medine (Jamal Salawu 55), Finley Craske, Angel Waruih, Will Jenkins-Davies, Scott Crocker (Oscar Massey 65), Rhys Shirley. Substitutes not used: Lewis Moyle, Ali Mansaray, Carlo Garside.