Tottenham welcomed Gent to Wembley looking to overturn a 1-0 deficit from the first leg, but they could only manage a 2-2 draw in a match that also saw Dele Alli sent off as the Belgian visitors picked up a famous victory in front of the largest Europa League crowd ever.
Like Spurs, Athletic Bilbao suffered a surprise exit from the competition as they fell to a 2-0 defeat at the hands of Cypriot side APOEL Nicosia to go down 4-3 on aggregate.
It was a particularly eventful game for Pieros Soteriou as he scored the opening goal before being sent off, but Bilbao failed to make the most of their numerical advantage and ended the game with 10 men themselves when Ander Iturraspe saw a late red.
Borussia Monchengladbach launched a stunning comeback to keep their Europa League dreams alive at the Stadio Artemio Franchi, with an 11-minute hat-trick from Lars Stindl helping the Bundesliga outfit to a 4-3 aggregate triumph over Fiorentina.
First-half goals from Nikola Kalinic and Borja Valero looked to have put the hosts out of sight following their 1-0 win in the first leg, but Stindl pulled one back from the spot right on the stroke of half time before adding two more within 10 minutes of the restart.
Andreas Christensen then scored on the hour mark to complete the fightback, seeing Monchengladbach progress in dramatic fashion.
There was to be no such comeback for Villarreal against Roma, however, as the Spanish outfit only managed a 1-0 win at the Stadio Olimpico despite Antonio Rudiger being shown a late red card for the hosts, who held out for a 4-1 aggregate victory.
Arguably the most dramatic of ties took place in Russia, with Zenit St Petersburg seemingly having done enough to overturn a two-goal deficit from the first leg only for Isaac Thelin's 90th-minute strike to put Anderlecht through on away goals despite a 3-1 defeat on the night.
There were more comfortable aggregate wins for Besiktas and FK Rostov as they cruised into the last 16 with minimal fuss, while Olympiacos, Ajax and Genk all joined them in the next round following first-leg draws.
FC Copenhagen managed to hold out for a goalless draw at home to Ludogorets to progress through courtesy of their 2-1 win in the first leg, but Shakhtar Donetsk fell just short of also holding out for an aggregate win as Iago Aspas's 90th-minute penalty forced extra time against Celta Vigo.
The Spanish side kicked on from that and, having been just minutes away from exiting the competition, ended up progressing into the next round courtesy of Gustavo Cabral's extra-time winner.
Thursday's Europa League last 16 results (aggregate score in brackets): Osmanlispor (0)0-3(3) Olympiacos; Ajax (1)1-0(0) Legia; APOEL (4)2-0(3) Athletic Bilbao; Roma (4)0-1(1) Villarreal; Besiktas (5)2-1(2) Hapoel Be'er Sheva; Zenit St Petersburg (3)3-1(3) Anderlecht - Anderlecht win on away goals; Copenhagen (2)0-0(1) Ludogorets; Fiorentina (3)2-4(4) Borussia Monchengladbach; Genk (3)1-0(2) Astra; Lyon (11)7-1(2) AZ; Shakhtar Donetsk (1)0-2(2) AET Celta Vigo; Sparta Prague (1)1-1(5) Rostov; Tottenham (2)2-2(3) Gent