South African Thulani Serero scored as Ajax Amsterdam became the first side to beat Barcelona this season.
Ajax won 2-1 in their Group H match on Tuesday to stay in contention for a place in the next round of the competition.
Serero and Danny Hoesen scored to give Ajax a surprise half-time advantage but straight after the break defender Joel Veltman was red carded for a tackle on Neymar and Xavi pulled a goal back from the penalty spot.
Injured-plagued Barcelona applied continuous pressure thereafter in search of an equaliser but Ajax held out to thunderous applause from a capacity Amsterdam Arena.
Ajax stay third in the group, one point behind AC Milan, who they must now beat away on Dec. 11 if they are to advance.
Barcelona still need one point to make sure of top place in the group but were already through to the knockout phase before Tuesday game.
Serero ghosted in late for the first goal in the 19th minute, applying the decisive touch to a strong cross from the right from fullback Ricardo van Rhijn, who just five minutes earlier had made a goal-saving tackle on Neymar.
The South African international’s first Champions League goal precipitated a period of sustained pressure from the young Dutch side, culminating in a second goal three minutes from half-time.
A poor clearance from Javier Mascherano saw Ajax set up a chance for Viktor Fischer, whose shot was parried by goalkeeper Jose Manuel Pinto, only for Hoesen to pick up the rebound, go round Carles Puyol and score with the help of a deflection off Gerard Pique.
But the comfortable cushion deflated just two minutes after the break when Van Rhijn’s poor back pass set Neymar away and Veltman tripped him on the dege of the area, conceding a penalty and getting himself sent off.
Xavi converted the spot kick to send Ajax into defensive mode as they tigerishly held on for the valuable three points, keeping Neymar at bay and ensuring the Brazilian has yet to open his Champions League goalscoring account.
It was Barcelona’s first defeat under new coach Gerardo Martino and ended hopes of a record-equaling longest unbeaten opening to the start of a season.
They last lost at home to Bayern Munich in last season’s Champions league semifinal.
