The home side led through a first-half goal from Hugo Colace, but the visitors struck back through Carl Fletcher, Jamie Mackie and Rory Fallon.
Plymouth might have claimed an early lead when Mackie played in a tempting ball from the right but Carl Fletcher's shot was a tame effort and ex-Barnsley striker Fallon was a fraction short of a scoring touch.
Barnsley midfielder Emil Hallfredsson blew a glorious early chance to give the home side the edge when he smashed a shot high and wide from ten yards after Jay Rodriguez won the ball and set him up on front of an open goal.
David Stockdale denied the home side when Rodriguez, who is on loan from Burnley, hit a superb shot from the edge of the area which forced the Plymouth keeper into a full-stretch save.
But seconds before the break, Barnsley crafted the advantage they had been searching for when Colace scored.
Carl Dickinson's cross from the left was deflected into the path of Argentinian Colace and despite mis-hitting his volley, it bounced past Stockdale.
Luke Steele pulled off a superb save five minutes after the restart to preserve the lead when he reacted smartly to turn away a powerful header from New Zealand international Fallon.
But Hallfredsson was only a fraction away from Barnsley's second when he drilled rasping shot just wide.
Plymouth, who were content to sit back in the first half, began to push for an equaliser and it came after 64 minutes when the ball broke to Fletcher, who crashed a thundering shot past Steele from the edge of the area.
Soon afterwards Plymouth were denied the lead when Damien Johnson struck a sweet dipping shot that beat Steele but smashed against the bar.
And 15 minutes from the end, Plymouth were celebrating when their pressure told and they went in front after Mackie headed in a corner from Yannick Bolasie.
Seven minutes before the final whistle, Fallon crowned the win with a spectacular third when he caught Steele off his line and swept in a clever shot from 35 yards.