Holders Atletico Madrid were knocked out of the Europa League at the last-32 stage despite defeating Rubin Kazan 1-0 in the second leg at the Luzhniki Stadium in Moscow.
A goal by Radamel Falcao in the 84th minute gave the visitors hope of overturning the 2-0 deficit from the first leg at the Vicente Calderon last week.
However, despite playing with a man extra in the final minutes of the game after Rubin Kazan captain Cesar Navas was sent off, they were unable to score again.
Inter Milan progressed courtesy of a 5-0 aggregate win over Romanian side Cluj.
Fredy Guarin scored twice and Marco Benassi added a late third as the Italians comfortably added to their 2-0 lead from the first leg.
Cluj were forced to play the closing minutes with 10 men following Mario Camora's dismissal.
Stuttgart eased into the last 16 with a 2-0 victory at Genk.
With the tie delicately poised at 1-1 following the first leg in Germany, goals from Arthur Boka and Christian Gentner saw the Bundesliga side through.
Basle are also safely into the next stage after a 3-1 aggregate win at Dnipro.
In an entertaining match, both teams netted late penalties and finished with 10 men but it was the Swiss visitors celebrating at the end of a 1-1 stalemate.
Trailing 2-0 from the first leg, Dnipro's hopes took a further nosedive when substitute Nikola Kalinic was sent off in the 63rd minute.
The hosts were handed a lifeline 14 minutes from time when Basle midfielder Fabian Frei handled inside the area, earning him an early bath and the home side a penalty from which Yevhen Seleznyov scored.
But five minutes later Basle's 10 men won a penalty of their own and Fabian Schar converted an away goal that killed off the tie.
Lazio comfortably progressed as first-half goals from Antonio Candreva and Alvaro Gonzalez downed Borussia Monchengladbach 2-0 for a 5-3 aggregate win.
Candreva sidefooted the hosts in front inside 10 minutes and Gonzalez's goal shortly after the half hour was enough to seal a routine win.
Viktoria Plzen beat Serie A title hopefuls Napoli for the second time in a week to book their place in the last 16 of the Europa League for the first time.
Plzen cantered to a 3-0 win in Naples last week and they completed a professional performance over two legs with a 2-0 victory thanks to strikes by Jan Kovarik and Stanislav Tecl.
Next up for Plzen is Fenerbahce, for whom Cristian Baroni's first-half penalty was enough see off 10-man BATE Borisov 1-0.
With the scores goalless after the first leg, BATE's hopes were hit by the dismissal of Dmitri Baga, while Cristian's spot-kick was enough to see Fener scrape through.
Benfica saw off Bayer Leverkusen 3-1 on aggregate in their encounter in Portugal.
Benfica held a 1-0 lead from the first leg in Germany thanks to Oscar Cardozo's goal, and their lead was doubled when Ola John found the net after an hour.
Andre Schurrle equalised for Leverkusen on the night with 15 minutes to go, but Benfica restored their two-goal cushion two minutes later through Nemanja Matic.
Benfica next play Bordeaux who progressed after a 2-1 aggregate win over Dynamo Kiev.
A solitary goal by Cheick Diabate shortly before half-time was enough to guide Bordeaux through after the first leg in Ukraine ended 1-1.
Anzhi Makhachkala set up a last 16 tie with Newcastle after surviving a scare against Hannover.
Trailing 3-1 from the first leg, Hannover threw everything they had at the Russians but only had Sergio Pinto's 70th-minute goal to show for it as Anzhi held on before Lacina Traore struck deep into stoppage time to earn a 1-1 draw on the night.
Levante are through to a tie with Rubin Kazan after a 1-0 win at Olympiacos.
The Spanish side held a 3-0 lead after the first leg and duly wrapped up a 4-0 aggregate win thanks to Obafemi Martins' early strike.
Steaua Bucharest sent Ajax crashing out after prevailing in a penalty shootout to set up a last-16 clash with Chelsea.
Ajax won the first leg 2-0 but Iasmin Latovlevici's first-half goal put Steaua ahead on the night and Vlad Chiriches struck from long range to make it 2-0 and force extra time.
Following a goalless extra-time period, Latovlevici netted the winning penalty after Lasse Schone and Niklas Moisander had missed for Ajax.