Rubin stunned the holders in Madrid, whilst Anzhi Makhachkala fought back from 1-0 down to beat Hannover 3-1.
Zenit St Petersburg also had an impressive victory, beating Liverpool 2-0. Elsewhere Chelsea beat Sparta Prague 1-0, Tottenham beat Lyon 2-1 and Inter Milan overcame CFR Cluj 2-0. Napoli were stunned 3-0 by Viktoria Plzen.