In a re-staging of a game that had been abandoned in November with Barnsley leading 4-1, both sides had their chances, but the Pilgrims will be ruing hitting the woodwork twice when on top in the first half.
Argyle had an early let-off when goalkeeper David Stockdale found himself blocked off in attempting to reach Adam Hammill's corner and was stranded in no-man's land as Ryan Shotton hooked the ball towards goal.
Fortunately for the Pilgrims, the full-back's attempt hit the crossbar and was cleared.
The woodwork at the other end came to Barnsley's rescue after Jamie Mackie broke away for Argyle and teed up Yala Bolasie from the byline, only for the winger's shot to cannon off a post.
Stockdale showed his other side when he reacted well to keep out a point-blank shot by Daniel Bogdanovic after Emil Halfredsson's cross had been deflected towards goal.
Argyle then hit the woodwork again when Reda Johnson found space in the Barnsley penalty area to get a clean head on Alan Judge's delicate free-kick but powered the ball against the crossbar.
Barnsley lost top scorer Bogdanovic to injury before a mistake by home defender Bondz N'Gala allowed Jon Macken a sight of goal, only for Stockdale to stop his low shot.
Argyle nearly broke the deadlock after the interval when Bradley Wright-Phillips battled to win possession and played in Mackie, whose shot was well saved by Luke Steele.
The see-saw game continued with Barnsley substitute Iain Hume breaking clear one on one with Stockdale, but the Canadian international scuffed his shot across the face of the Argyle goal.
Hume was then denied by Stockdale after he found space to run into with Argyle pushing for a goal that would have kept their season alive but that would not come.