Calvin Andrew had been on the pitch for only four minutes - and had only come off the bench because of an injury to Markus Heikkinen -when he slid home the winner from close range.
Andrew had been set up by fellow sub Rowan Vine who had inspired the comeback after volleying home an equaliser following good work from skipper Steve Howard.
Argyle had looked to be on their way to victory when their own substitute Akos Buzsaky, who has not started a game since January, lashed home a left-foot 70th minute shot.
Prior to the Hungarian's piece of skill, the Pilgrims appeared to have been the victims of a controversial refereeing decision.
On-loan Portsmouth forward Vincent Péricard felt he had headed home captain Paul Wotton's excellent left-wing cross that Luton goalkeeper Marlon Beresford failed to collect first time.
The ball seemed to have crossed the line before Beresford collected it at the second attempt but referee Andy Hall incurred the wrath of the Argyle bench by deciding it was no goal.
Argyle gave a season's debut to goalkeeper Luke McCormick and he needed to be on his toes to keep out a shot from Howard just before the interval after Warren Feeney had profited from a mistake by Mathias Doumbe.
Luton, who overcame a lengthy injury-list to become only the second side to score more than one goal against the Pilgrims this year, came close to going behind in the second minute when Péricard set up Leon Clarke who headed wide.