Big-spending Zenit St Petersburg were knocked out by Basel, while Fenerbahce, Benfica and Rubin Kazan advanced to the last eight
Fenerbahce survived a late scare at the Sukru Saracoglu on Thursday to draw 1-1 with Viktoria Plzen and progress to the quarter-finals of the Europa League.
The Turks - on the back of a crucial 1-0 first-leg victory on the road - took the lead on the stroke of half-time when Cristian's cut-back found Salih Ucan, who applied a simple finish from close range.
And although they were made to sweat for their place in the last eight, as Vladimir Darida levelled on the hour mark, Fenerbahce rode out the storm.
BORDEAUX 2-3 BENFICA (agg 2-4)
Benfica ran out 3-2 winners over Bordeaux to book their place in the Europa League quarter-finals.
On 30 minutes, the Eagles took the lead and grabbed a crucial away goal thanks to Jardel's header from Ola John's corner, but Cheick Diabate's close-range strike restored equilibrium midway through the second half.
Just a minute after les Girondins' attempts to work their way back into contention, Oscar Cardozo slipped a cool finish past Cedric Carrasso from Nicolas Gaitan's clipped ball, although Jardel turned from hero to villain in stoppage time with an own goal.
Nonetheless, Cardozo pounced to net his second of the match and send Benfica into the next round.
ZENIT 1-0 BASEL (agg 1-2)
Zenit St Petersburg's European adventure for the season is over after they failed to overturn a 2-0 first-leg deficit, despite running out 1-0 winners on the night.
The Swiss side took a 2-0 lead into the second leg, hosted in Russia, but they went behind inside half an hour when Hulk's corner deflected off Nicolas Lombaerts and eventually found Axel Witsel at the near post.
Basel's then had cause for concern following Marcelo Diaz's red card for a second bookable offence, but they hung on thanks to Roman Shirokov's missed penalty at the death.
RUBIN 2-0 LEVANTE (agg 2-0)
Rubin Kazan took full advantage of home comforts in the second leg of their last-16 tie with Levante after they ran out 2-0 winners on Thursday,
Neither side could break the deadlock over 90 minutes, but Salomon Rondon fired home in extra time from Bebras Natcho's lobbed through pass.
And the hosts doubled their lead 10 minutes later when a long throw was read and consequently buried by Vladimir Dyadyun.