Plymouth super subs Martin Phillips and Ian Stonebridge rescued three precious points for the second-placed Pilgrims, who were ten minutes away from losing at home for only the second time this season.
Stonebridge netted the winner in the fifth-minute of injury-time after Phillips' 80th-minute equalizer as all Vale's brave efforts came to nothing.
It had looked so different for the promotion-chasing Potteries team, who took the lead through Steve McPhee's breakaway goal nine minutes after half-time.
McPhee had been set up by Steve Brooker, who robbed Argyle captain Graham Coughlan on the left touchline before sprinting in and squaring for his fellow forward to convert.
It was the first goal the Pilgrims - without a win in their previous three matches - had conceded at Home Park since November 1.
Argyle laid siege to the Vale goal after going behind, but it seemed as though, with the help of the crossbar and some excellent defending, they would hold out.
It took a left-foot screamer from Phillips, latching smartly on Mickey Evans headed flick-on, to break their resistance, the ball crossing the line via the crossbar, although Billy Paynter was booked for disputing the decision.
Vale goalkeeper Jonny Brain then made a tremendous save to deny Phillips a second, and Hasney Aljofree hit the post with a 25-yard free-kick as Argyle poured forward.
Their persistence was rewarded in the 95th minute of play when Phillips chased to keep the ball in play and Paul Connolly's cross was slid past Brain for a dramatic later winner.
With QPR failing top beat Peterborough on Friday, the victory leaves Argyle four points clear in second place, still one point behind Bristol City.