The loss, however, did nothing to harm Chelsea's progress to the Round of 16 as Steaua Bucharest held Schalke to a 0-0 draw in Romania allowing the Londoners to remain top of Group E with one fixture remaining.
Jack Wilshere scored a double for the Gunners who despite recording 12 points - three more than the Blues - have not yet qualified for the next phase after Borussia Dortmund beat Napoli 3-1 to join the Italians on nine points.
Arsenal now need to avoid a 3-0 loss to Napoli in Naples on December 11 to ensure their path through while Dortmund will qualify if they can get at least a point when they travel to Marseille on the same date.
The Dutch club shocked the Blaugrana at Amsterdam ArenA with first-half goals from Thulani Serero and Danny Hoesen doing the early damage before Xavi pulled one back from the penalty spot early in the second half.
And in Group G, the already-qualified Atletico Madrid drew 1-1 with Zenit St Petersburg in Russia, while Austria Vienna missed out on the chance to progress when they drew 1-1 with FC Porto who now sit one point behind Zenit in third spot.
2013/14 UEFE Champions League group stage scores
Steaua Bucharest (ROM): 0 Schalke (GER): 0 Arena National, Bucharest, Romania - 50,633
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