It was Real's first defeat of the season and left them lying sixth in La Liga without a Spanish league away win since March. Vicente del Bosque condemned as their worst performance since he became coach three years ago.
Despite having Zivkovic dismissed in the first half for two bookable offences Bayer Leverkusen beat Kaiserslauten one nil with a twentieth minute goal from Bradic. The win took Lverkusen out of the bottom three.
The continuing disputes in the Greece and Israel meant that there were no games for Haifa or Olympiakos.
Rivaldo scored his first goal for his new club as AC Milan won won 4-1 away at Atalanta, taking them above Inter at the top of Serie A. Inter lost their one hundred per cent record in a 1-1 home draw with Juventus, in a match which saw two goals and two sending offs in the final two minutes.
In France, Auxerre, who visit Arsenal in the Champions League tomorrow, lost 3-0 at Olympique Lyonnais with Brazilian Juninho Pernambucano bagging a hat-trick.