Walter Mazzarri's side exited the competition 5-0 on aggregate, while elsewhere, there were wins for Levante, Bordeaux and Benfica
Stuttgart comfortably booked their place in the next round with a 2-0 victory over Genk at the Cristal Arena in Belgium.
The German outfit started decently, with the nagging thought of having to score tonight following Genk's away goal at the Mercedes-Benz Arena last week.
Nevertheless, it took until just before the half-time interval for the opening goal to be scored in fortuitous circumstances. Arthur Boka took advantage of a heavy deflection off Anele Ngongca to power in the opener, as well as putting hiss ide ahead on aggregate.
Stuttgart improved after the break, and doubled their tally soon after. The Belgian side failed to deal with a flowing move, allowing Christian Gentner to fire in a left-footed shot to enable some breathing space.
The hosts failed to threaten the opposition seriously, as the visitors held on to confirm a tie against Serie A side Lazio.
DNIPRO DNIPROPETROVSK 1-1 FC BASEL (1-3 AGG.)
FC Basel weathered the Dnipro storm late on to confirm a place in the Europa League last 16 thanks to a 1-1 draw which sees them safely through 3-1 on aggregate.
Despite a rather turgid first half, it seemed Dnipro's chances had evaporated just after the hour mark when Nikola Kalinic was shown a red card.
But despite that setback, they still managed to open the scoring. Roman Zozulya's shot was charged down by Fabian Frei, who was also sent off before Yevhen Seleznyov stroked the ball home to hand Dnipro a boost with 14 minutes remaining.
With both sides down to ten men, the next goal would come in almost the same circumstances. Zozulya this time conceded a penalty for a foul on Valentin Stocker, allowing Fabien Schar to equalise with the important away goal from the spot, and kill the tie off once and for all.
Basel progress where they will play Zenit St-Petersburg.
LAZIO 2-0 B MONCHENGLADBACH (5-3 AGG.)
Lazio saw off the challenge of Borussia Monchengladbach, sealing a 2-0 win to confirm a 5-3 aggregate victory at Stadio Olimpico.
Following on from last week's frenetic 3-3 draw at the Borussia-Park, it took just 10 minutes for the deadlock to be broken in the Italian capital.
Alvaro Dominguez was caught on the ball, allowing Antonio Candreva to steal in and direct the ball past Marc-Andre ter Stegen to hand the Serie A side the lead.
It wasn't long before the advantage was doubled, just after the half-hour as Vladimir Petkovic's side dominated their German counterparts. Ter Stegen saw off Stefan Radu's threatening shot, but he could only divert the ball back in play, into the path of Alvaro Gonzalez to cement a commanding 5-3 aggregate lead.
Lucien Favre's men failed to inspire on the night, and will rue their limp performance as Lazio progress to a last 16 tie away to Stuttgart in two weeks' time.
FENERBAHCE 1-0 BATE BORISOV (1-0 AGG.)
Fenerbahce finally saw off the challenge of a stubborn BATE Borisov outfit, as they qualified courtesy of a 1-0 win on the night.
With last week's clash in Minsk ending 0-0, the onus was on both sides to strike up the lead on aggregate in a competitive start in Istanbul. Though, like the Turkish outfit in the first leg, BATE would also see a man sent off early on.
Dimitri Baga picked up two yellow cards within four minutes to receive his marching orders, before Cristian saw the hosts into the lead from the penalty spot just before the half-time whistle, which proved to be the matchwinner at Sukru Sacroglu.
Fenerbahce will travel to Viktoria Plzen for the first leg of their round of 16 tie on March 7.
OLYMPIAKOS 0-1 LEVANTE (0-4 AGG.)
An early goal from Obafemi Martins allowed Levante to put the second leg to bed after just nine minutes, as they beat Olympiakos 1-0 to complete a 4-0 aggregate victory.
The Spanish outfit had done much of the damage in last Thursday's first leg, picking up a resounding 3-0 win, though that did not deter them from starring early on in Piraeus.
A corner - drifted in from the right - got the better of a static Greek defence, allowing Martins to glance in a header unchecked after nine minutes on the clock.
The hosts were already realistically out of the tie by that point, and failed to claim a consolation goal, as the visitors held firm to progress.
Levante will now turn their attention to a last 16 tie against Premier League side Newcastle United.
BORDEAUX 1-0 DYNAMO KIEV (2-1 AGG.)
Bordeaux remain the final Ligue 1 club left in the Europa League as they narrowly edged out Dynamo Kiev to seal a place in the next round.
The French side were reeling from their heavy 4-0 defeat to Olympique Lyonnais at the weekend, but started the brighter at the Stade Chaban-Delmas.
Francis Gillot's outfit took the lead just before half-time from a set-piece situation. Benoit Tremoulinas' cross took a touch off Gregory Sertic, and into the path of Cheickh Diabate who ultimately bagged the game's only goal of the evening.
Bordeaux entertain Benfica in the last 16.
BENFICA 2-1 BAYER LEVERKUSEN (3-1 AGG.)
Benfica booked a last 16 clash against Ligue 1 outfit Bordeaux after a comfortable 2-1 win over Bayer Leverkusen at Estadio da Luz.
The Eagles were already ahead on aggregate, given their slight advantage in Germany last week, but went ahead just before the hour mark through Ola John, who nudged Jorge Jesus' men ahead, as they sought to put clear daylight between them and the Bundesliga side.
The visitors, however, failed to be consigned to their fate, with Andre Schurrle equalising - a just reward for his efforts this evening - firing in from Arkadiusz Milik's pass.
However, the Portuguese outfit instantly regained the lead, as Lima's threatening cross was picked up by midfielder Nemanja Matic, who all but sealed Benfica's passage.
HANNOVER 96 1-1 ANZHI MAKACHKALA (2-4 AGG.)
Anzhi Makhachkala required a 99th minute equaliser in Germany, but nonetheless saw off Hannover 4-2 on aggregate to progress.
The German side were seeking to come back from a 3-1 deficit in the first leg, but finally initiated a breakthrough in the second half.
Szabolcs Huszti's brilliant delivery down low picked out Sergio da Silva Pinto, who arrived into the box unmarked to fire into the Anzhi net and set up a grandstand last few minutes in Germany.
However, that failed to materialise as Guus Hiddink's side managed to score in the ninth minute of injury time through Lacina Traore to conjure up a last 16 tie against Newcastle United.
VIKTORIA PLZEN 2-0 NAPOLI (5-0 AGG.)
Viktoria Plzen breezed past Serie A side Napoli, picking up a 1-0 win on the night to seal a resounding 4-0 win on aggregate.
Following on from their shock 3-0 win at the Stadio San Paolo in the first leg last week, the previously unfancied Czech outfit were heavy favourites to get the job done, and looked comfortable in a competitive first half.
Nevertheless, they did compound further misery on Walter Mazzarri's side, taking the lead on the night soon after the interval. Frantisek Rajtoral's delivery was converted in by Jan Rovarik, with Morgan De Sanctis unable to keep out the effort.
Stanislav Tecl added in a second midway through the second half to complete a fabulous victory over the Partenopei, as they look towards a clash against Fenerbahce.
STEAUA BUCHAREST 2-0 AJAX (2-2 AGG. 4-2 PENS.)
Steaua Bucharest completed a remarkable comeback to progress past Ajax, first halving the aggregate deficit seven minutes before the break through Iasmin Latovlevici, who showed brilliant composure to latch onto Florian Gardos' pass and put Steaua ahead on the night.
Frank de Boer's side were lethargic and profligate for large periods, and were punished once more, as Vlad Chiriches hauled Steaua back on level terms on aggregate with a sumptuous strike from outside the area to take the game to extra time.
With neither side able to break the deadlock during the two 15-minute periods, the game went to spot kicks.
And it was the home side who held their nerve, winning the shoot-out 4-2 after Niklas Moisander and Lasse Schone missed for the Dutch side to send them crashing out of the competition.