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.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.