Having trailed to Kayden Jackson's penalty, a brace from Arvin Appiah put The Reds in front in South Yorkshire and despite Matty Wolfe's second-half equaliser for the home side, Forest came on strong and secured the points thanks to a double from Virgil Gomis.
The Reds put in some strong challenges in the early stages as both Choz Charlesworth and Danny Preston were cautioned for their efforts before Barnsley's Jacob Brown came close with a rifled drive from the edge of the area.
There were opportunities for both sides as Gomis brought the best out of goalkeeper Jack Walton and Jackson shot wide from a tight angle but it was The Tykes who broke the deadlock from the penalty spot with three minutes of the first half to play.
Jackson was adjudged to have been brought down by Anel Ahmedhodzic inside the box and the Barnsley men dusted himself down to send Jordan Wright the wrong way from 12 yards to give the hosts the half-time advantage.
That lead only last five minutes into the second half as Appiah drove the ball into the back of Walton's net before the same man put Forest in front nine minutes later as he smashed the ball into the back of the net from a tight angle.
Barnsley responded strongly as Wright was forced to make a point-blank save from a Ben Williams header but there was nothing The Reds' stopper could do when Wolfe lashed in a strike from close range moments later.
The game was swinging one way then the other and with three minutes of normal time remaining, Forest made it 3-2 as Gomis was able to stab the ball home from inside the six-yard box following a superb initial save from Walton.
Jack Lester's side then wrapped up the points in second-half stoppage time as Gomis stepped up to slot home a penalty after substitute Luke McCormick had gone down under Walton's challenge inside the box.
Forest: J.Wright, Charlesworth, Preston, Edser (C.Smith 90'), Ahmedhodzic, Iacovitti, Walters (McCormick 66'), Crookes, Gomis, Appiah, En-Neyah
Subs not used: Shelvey, Taylor, Harbottle