Liverpool were brought down to earth in the Europa League after losing 1-0 at Sporting Braga in Portugal in the last 16, while big-spending Manchester City crashed 2-0 at Dynamo Kiev of the Ukraine.
Liverpool, rejuvenated under new coach Kenny Dalglish and 3-1 victors over arch-rivals Manchester United last weekend, will have to turn their tie around in next week's return leg if they are to reach the quarter-finals.
City completed an underwhelming evening for the English sides as they went down 2-0 amid freezing conditions in the Ukrainian capital.
Portuguese champions Benfica had to dig deep as they fought back from a goal down to beat Paris Saint-Germain 2-1 at the Estadio da Luz.
Dutch champions FC Twente took a sizeable step towards the last eight after a 3-0 win at home to 2008 champions Zenit Saint-Petersburg.
Spartak Moscow struck a blow for their country in the night's other Dutch-Russian encounter, however, by prevailing 1-0 at Ajax.
Villarreal asserted control of their tie against Bayer Leverkusen as a goal in the fourth minute of injury time earned them a last-gasp 3-2 victory in the away leg.
Elsewhere, Portuguese league leaders Porto won 1-0 at CSKA Moscow, while Scottish champions Rangers' visit to PSV Eindhoven finished goalless.