Torrential rain caused the original November fixture to be abandoned in controversial circumstances with Barnsley 4-1 ahead, and FA Cup commitments followed by another waterlogged pitch necessitated further rescheduling.
Argyle, who are five points shy of safety with as many games remaining, enjoyed long periods of dominance in an absorbing encounter, but they were indebted to goalkeeper David Stockdale who pulled off a string of fine saves as Barnsley fashioned the clearer openings.
The pace of Yannick Bolasie and Bradley Wright-Phillips had Plymouth on top in the opening exchanges but the visitors almost opened the scoring in the 11th minute.
Adam Hammill's corner evaded Stockdale and on-loan Stoke defender Ryan Shotton was unlucky to see a spectacular overhead kick cannon back off the crossbar.
The home side responded through Jamie Mackie, who slipped past challenges from Hugo Colace and Stephen Foster before dragging wide, and they tested the woodwork themselves after 18 minutes.
Mackie got in behind the Barnsley defence and squared to Bolasie whose shot bounced to safety off the angle of post and bar.
In the 24th minute, Barnsley's Emil Hallfredsson cut in menacingly from the right flank and his goal-bound shot was deflected into Daniel Bogdanovic's path, forcing Stockdale to spring from his line and save from point-blank range.
Hammill then skilfully engineered room to deliver a teasing cross, which Colace glanced narrowly wide after timing his late run into the area perfectly.
After 35 minutes Plymouth's Reda Johnson headed Alan Judge's free kick against the crossbar after Shotton brought down Onismor Bhasera.
A defensive lapse from Bondz N'Gala let in Macken two minutes before the interval and Stockdale had to produce an impressive stop.
Argyle started brightly after the interval with Bolasie's trickery causing Shotton particular problems.
In the 50th minute Tykes keeper Luke Steele pulled off a superb reaction save from Mackie after good link-up play with Wright-Phillips.
Barnsley sprung to life midway through the half and substitute Iain Hume found himself one on one with Stockdale thanks to Macken's measured pass, but Stockdale was equal to the task once more.
In the 68th minute a wonderful pass from Argyle sub Joe Mason split the Tykes defence and Mackie cut inside Shotton to drill in a low shot which Steele grasped at the second attempt.
Stockdale came out on top in another one-on-one with Hume after the Canadian caught Karl Duguid napping to spring the offside trap with 12 minutes remaining.
The on-loan Fulham stopper then saved Colace's 30-yard effort in a more unconventional fashion, palming the Argentinian's shot against the crossbar before gratefully clutching the rebound.
In stoppage time, N'Gala almost won it for Argyle, forcing Steele to tip his snap-shot over at full stretch.