Devaney's first came from 25 yards, just after the half-hour mark, by which time Tykes team-mate Lewin Nyatanga had already cancelled out another fine strike by Pilgrims captain Lilian Nalis.
That paled into insignificance compared to his second after an hour which came when Argyle had been able to go into the break on level terms through Sylvan Ebanks-Blake's tap-in.
Devaney crashed a drive past Argyle goalkeeper Luke McCormick from the best part of 50 yards to thoroughly stun the home side, who have now taken just three points out of a possible 12, and crashed out of the FA Cup, all inside a few weeks.
A goal in second-half stoppage time from Hungary international Istvan Ferenczi completed the Tykes' fine night.
Argyle, beaten 1-0 by Watford on Sunday in the last eight of the FA Cup, showed no signs of a hangover as Nalis swept home David Norris' square pass from 25 yards in the 15th minute.
Five minutes later, the unmarked Nyatanga rose to head Brian Howard's corner past McCormick.
Peter Rajczi then set up Devaney for his first, crossing the ball across the Pilgrims' penalty area, where Devaney was lurking unmarked to whack the ball past McCormick from 25 yards.
Howard then sent a thunderous drive against the crossbar before Ebanks-Blake stole in to finish off a scrap in the Barnsley penalty area caused when Nalis' header hit a post.
Devaney's second of the game, on the hour mark, was a staggering strike, even when compared to his amazing first-half shot. He picked up the ball in midfield, looked up, and crashed the ball past McCormick from way out.
Argyle substitute Bojan Djordjic saw a shot cleared off the line by Sam Togwell before a tired Norris lost possession to give the Tykes a three-on-one advantage which Ferenczi finished off.