Andy Ritchie's side had started brightly - and had deservedly gone in front after five minutes through striker Paul Hayes - but they then failed to take advantage of other chances and were left rather nervously trying to see out the closing minutes.
Darlington, who had hit the bar in the first half, suddenly went very direct following a substitution which saw Guylain Ndumbu-Nsungu sent on up front.
The former Sheffield Wednesday player made an immediate impact as the visitors began to hit high ball after high ball into the Barnsley box.
Ndumbu-Nsungu was unlucky with a great left-foot volley eight minutes from time that brought a smart full-length save from Barnsley keeper Nick Colgan.
Three minutes later Ndumbu-Nsungu went even closer, his shot from six yards somehow bringing a stunning reflex stop from Colgan right on the goalline before being hurriedly cleared.
But with Bobby Hassell and Neil Austin in determined mood for Barnsley at the back, Darlington's hopes were finally extinguished.
Barnsley had started in positive fashion, forcing six corners inside the opening 10 minutes.
They made a breakthrough in the fifth minute when Chris Shuker's cross from the right fell perfectly into the path of Hayes and he galloped clear to lob advancing keeper Sam Russell for his fifth goal of the season.
The rest of the half was rather flat, although Martin Devaney twice went close for the home side and Darlington winger Neil Wainwright clipped the bar with a stabbed shot.
Barnsley also had chances after the break to put the tie to bed but Russell made smart saves from Hayes and Marc Richards, while Devaney sent a couple of fierce drives just over.
Darlington then began to hit the ball long in a desperate attempt to snatch an equaliser but for once the Barnsley defence stood firm.