The 10 men Reds fell to defeat in the Sky Bet Championship as Fulham's late show took all three points back to West London.
Barnsley began the game on the front foot, pressing Fulham high and getting the fans right behind them.
Just three minutes into the match saw a great layoff from Kieffer Moore, making his first Oakwell start, perfectly into the path of Stevie Mallan 30 yards out, whose great first touch allowed him space to bend an effort towards the top right-hand corner which saw Marcus Bettinelli have to stretch and tip behind the post for a corner.
Whilst the Reds were pressing well, they were creating good breaks without truly profiting.
On 15 minutes, Fulham were given a free-kick 30 yards from goal and it was Stefan Johansen who sent the resulting shot well wide.
Eight minutes later and a Moore flicked header from Dimitri Cavare’s throw-in dropped onto the roof of the net.
But the goal the Reds deserved came on the half hour mark, and it was a first for the club for Liam Lindsay.
He was on hand from a wicked Mallan corner to score low into the bottom corner at the second attempt after an initial save by the ‘keeper’s legs.
Just a minute later and it could have been two with Tom Bradshaw through on goal and about to strike inside the box when Ryan Fredericks intercepted last minute and cleared.
Adam Hammill and Dimitri Cavare both entered the referee’s notebook, earning yellow cards for reckless tackles as Fulham looked to hit back before half time.
Hammill then saw a dipping volley from the edge of the box saved by Bettinelli.
But right before half time the Reds were reduced to 10 men when Cavare, after being fouled himself reacted by pushing Johansen, forcing the referee to show him a second yellow card before the red.
HALF TIME: Barnsley 1-0 Fulham
Dani Pinillos made his Reds debut replacing Bradshaw at half time.
Fulham equalised in the 50th minute when Sessegnon fired in low beyond Adam Davies after an initial shot had struck the post.
Lindsay was next into the busy referee’s book, after pulling back Lucas Piazon on halfway. It was all Fulham by now and looking a matter of time until they took the lead.
On 58 minutes the Reds showed some fight with Hammill leading the charge forward, but after some uncertainty in defence, Fulham eventually cleared their lines.
Paul Heckingbottom replaced Hammill with the back-from-injury Ryan Hedges on the 65th minute.
As the supporters remembered Patrick Cryne on 66 minutes, the players responded, forcing consecutive corners but the Fulham backline held firm.
With just over 10 minutes remaining, Ryan Hedges set off on a trademark run towards the box beating men, but his powerful shot as he approached the box was turned away by the ‘keeper.
Davies was then thrust into action, diving low to his left to turn behind a Fulham effort. It was end to end and looking unlikely to finish 1-1.
81 minutes on the clock and Hecky made his final change, with the hard-working Moore replaced by Mamadou Thiam.
With five minutes left to play, the visitors went close through Kevin McDonald who curled an effort just over the bar from the edge of the box.
But in the third minute of five added at the end of the game, Fulham scored a disputed winner.
A cross was headed straight at Davies who turned it up into the air, the ball fell and bounced around the goal-line allowing the Reds ‘keeper to claim, but the goal was given by the linesman.
And it was game over a minute later when Fulham hit the Reds on the break, a cross by Kamara was missed by Lindsay and Sessegnon was there to tap into an empty net for 1-3.
FULL TIME: Barnsley 1-3 Fulham
Reds XI: Davies; Cavare, Pearson, Lindsay, Yiadom; Hammill (Hedges 65), Gardner, Mallan, Moncur; Moore (Thiam 86), Bradshaw (Pinillos 46).