The young Amsterdam team dominated the first half against a Barcelona side that had already qualified for the knockout stages and took a well-deserved 2-0 lead into the break thanks to goals from Thulani Serero and Danny Hoesen.
But Ajax gifted Barcelona a way back into the Group H match almost immediately after the break when Joel Veltman brought down Neymar, earning the central defender a red card and Barcelona a spot kick that Xavi Hernandez calmly converted.
Ajax is vying with AC Milan on the last day of group play for the second spot.
Chelsea qualified for the knockout stages of the Champions League despite losing 1-0 to Basel after a late strike by Mohamed Salah gave the Swiss side a deserved victory.
Chelsea has nine points in Group E, followed Basel on eight and Schalke with seven after the German side was held to a 0-0 draw at Steaua Bucharest on Tuesday.
But the fact that Basel and Schalke meet each other in the final round of matches means that only one of those clubs can overhaul Jose Mourinho's group leaders.
Salah sprinted clear of Chelsea's defense to clip a left-foot shot over the advancing Petr Cech and complete home and away wins for the Swiss team against the 2012 European champion.
-AP