Carlton Morris gave the Tykes the lead rom the penalty spot late in the first half but Fulham’s sustained pressure finally told late on with a delectable Wilson effort.
The Whites continued to move forward with lightning pace and Carvalho saw his effort roll just wide of Brad Collins’ post after some brilliant play down the left side.
A poor header from Mitrovic allowed Morris to try his luck with an effort on goal but his 20-yard strike did not trouble Marek Rodak and rolled wide of the mark.
After the pulsating start, the game descended into a scrappy affair with both teams arguing with referee Tim Robinson’s decisions.
The change in flow seemed to suit the hosts and they came close to breaking the deadlock through Remy Vita. A cross fell to the winger at the back post and his shot across the face of goal deflected off the knee of Morris before Tim Ream cleared off the line.
An uncharacteristic mistake from Tosin Adarabioyo in the 44th minute allowed Morris to close in on the Fulham goal before he was upended by the aforementioned defender.
Morris dusted himself off and slammed the penalty straight down the middle to beat Rodak and give the Tykes the lead.
The striker almost claimed a second in the dying embers of the half – his chip beat Rodak but Ream hooked the ball away from goal with a last-ditch clearance.
Marco Silva made a change during the break as he brought on Tom Cairney to replace Jean Michael Seri.
The change almost paid off immediately when Cairney, Neco Williams and Wilson played some nice stuff down the right before Carvalho blasted over after Mitrovic knocked the ball down from a cross.
Decordova-Reid continued to look lively down the left side of the Fulham attack. The attacker fired a golden chance over from close range just after the hour mark.
With the game reverting back to a scrappy affair, both sides made changes to inject some energy. Romal Palmer and Ivan Cavaleiro replaced Matty Wolfe and Harrison Reed respectively.
The league leaders hunted for a way back into the game and found a leveller in the 86th minute, Wilson unleashing an unstoppable curling effort past the outstretched arms of Collins.
Wilson almost won it in stoppage time but could only put his header agonisingly wide with the goal gaping.