The lead belonged to the hosts in the 12th minute when Alberto Aguilar lost his marker at a free kick to convert from close range.
Sandro Ramirez equalised for Barcelona midway through the first half when he latched onto a loose ball before firing home from a tight angle.
Adama Traore, who signed a new contract with the Catalan club earlier this week, put the visitors in front with an emphatic finish after evading a couple of challenge on his way into the box.
Barcelona scored a third just before the interval through Alen Halilovic, who used the space on offer 25 yards from goal to curl an effort into the top corner.
Ponferradina piled the pressure on in the second half, and they finally reduced the deficit in the 71st minute when Alcoron broke free of the visiting defence before slotting the ball home.
The game appeared to be over three minutes later when Oscar Ramirez, under pressure at the front post, inadvertently diverted the ball into his own net to hand Barcelona a 4-2 lead.
However, Ponferradina somehow managed to produce a remarkable response as Yuri found the net twice in as many minutes to secure a dramatic point for the hosts.