Holders Atletico Madrid bowed out of the Europa League on Thursday, losing 2-1 on aggregate to Rubin Kazan, as Tottenham and Chelsea advanced.
Atletico lost 2-0 at home to Russian Premier League Rubin in the first leg of their round-of-32 tie last week.
A goal from star striker Radamel Falcao saw the visitors from Spain win the return fixture 1-0 at the Central Stadium, but it was not enough for Diego Simeone's men to continue their defence of the trophy.
Chelsea, meanwhile, had been staring down the barrel of extra time in their second-leg match against Sparta Prague at Stamford Bridge, with Sparta leading 1-0 on the night to see the tie locked at 1-1 on aggregate deep into the second half.
But a 92nd-minute strike from Eden Hazard was enough to give Rafael Benitez's men a 1-1 draw and a 2-1 aggregate win.
Tottenham progressed thanks to a last-minute goal from Mousa Dembele in their match away to Lyon.
Spurs had won the first leg 2-1 at home, but trailed 1-0 in the return after Maxime Gonalons struck for the hosts in the first half at the Stade de Gerland.
With the tie level at 2-2, Lyon looked set to progress on the away goals rule, before Dembele's late effort sent Tottenham through 3-2 on aggregate.
They will meet Inter Milan in the round of 16 after the Serie A heavyweights downed Romanian side CFR Cluj 3-0 away from home, sealing a comprehensive 5-0 aggregate win.
Liverpool, meanwhile, were knocked out of the tournament despite a thrilling second-leg against Zenit St Petersburg at Anfield.
Trailing 2-0 after the first leg in Russia, Liverpool looked gone when Hulk scored for the visitors on 19 minutes.
But a double from Luis Suarez and a goal for Joe Allen had the tie all square at 3-3 on aggregate just before the hour mark.
Zenit held on, however, to progress to the last 16 on the away goals rule.
Newcastle United extended their run in the competition with a 1-0 win away to Metalist Kharkiv, after the first leg in England ended 0-0.
A penalty from veteran striker Shola Ameobi in the 64th minute at Metalist Stadium proved the difference between the teams.
Lazio of Serie A and Bundesliga outfit Borussia Moenchengladbach played out a thrilling 3-3 draw during their first leg in Germany last week, but a more routine 2-0 home win at the Stadio Olimpico saw the Italian side advance.
Napoli failed to make any inroads into their 3-0 deficit after the disastrous first leg against Viktoria Plzen in Naples, going down 2-0 in the Czech Republic for a comprehensive defeat.
Bayer Leverkusen were eliminated by Portuguese heavyweights Benfica, with their 2-1 loss in Lisbon on Thursday confining the Germans to a 3-1 aggregate defeat.
Elsewhere, Stuttgart defeated Genk 2-0 away from home to go through 3-1 on aggregate, while Basel managed a 1-1 draw at Dnipro Dnipropetrovsk, the Swiss side also going through 3-1.
Russian outfit Anzhi Makhachkala were too good for Hannover, taking a 1-1 draw in Germany in the second leg for a 4-2 victory on aggregate, and a penalty just before half-time from Cristian Baroni gave Fenerbache a 1-0 triumph over BATE in Turkey to seal their progress.
Spanish club Levante's 1-0 away against Olympiakos Piraeus fired them to a 4-0 aggregate victory while Bordeaux's Cheick Diabite scored to give the French club a 1-0 win over Dynamo Kiev in France after a 1-1 draw in the first leg.