Paul McGuinness' line-up was much-changed after the Reds' FA Youth Cup exertions against Charlton on Wednesday evening, with Jack Barmby and Tyler Blackett on the bench, while Mats Daehli and Gyliano van Velzen were rested entirely.
Keen to exploit the changes in personnel and the likelihood of tiredness in those starting for the visitors, Barnsley's energetic pressing game reaped dividends.
The hosts made a bright start and took the lead on 17 minutes, when Abbott capped a neat move by effortlessly curling an unstoppable shot into Joe Coll's top corner from just inside the United area.
Thereafter, the Reds were never given time in possession as the hosts maintained a high-tempo approach with and without the ball.
United's best opportunities were limited to set pieces, as Kenji Gorre curled a 25-yard effort just wide of the post, while substitute Jack Rudge's deflected free-kick was finger-tipped just over the bar by Lukas Lidakevicius.
The Reds' cause was further hindered by injuries. Rudge had replaced Sam Byrne after the striker suffered a blow to his ankle, while Charni Ekangamene and Matt Wilkinson both received bruised hips within seconds of one another.
United started the second period brightly, and were unfortunate not to receive a penalty when Kurtis Turner halted Gorre's run with a clumsy handball inside his own area, but it was the hosts who looked likelier to bag the game's second goal during their late forward forays.
Clear-cut chances were at a high premium for both sides