West Ham edged Sevilla in extra time, while Atalanta and Barcelona won on the road to progress. Europa League quarter-final draw takes place on 18 March.
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Six-time UEFA Cup/UEFA Europa League winners Sevilla will not be adding to their haul after West Ham overturned a first-leg deficit to knock out the Spanish side, while Atalanta and Barcelona scored victories away from home to advance.
UEFA.com rounds up the Europa League round of 16 deciders after eight clubs booked their places in Friday's quarter-final draw.
Eintracht Frankfurt (GER)
West Ham (ENG)
Crvena zvezda 2-1 Rangers (agg: 2-4)
Rangers reached the last eight of a European competition for the first time in 14 years despite a narrow defeat at Crvena zvezda. The home side trailed 3-0 after the first leg but flew out of the blocks and went ahead when Mirko Ivanić was left unmarked at a corner, chesting down before volleying past Allan McGregor.
McGregor was the star turn in the first leg and was at it again here with a number of fine saves in either half, the best of them to deny substitute El Fardou Ben Nabouhane. By then, though, Rangers had got their goal, a fine solo strike by Ryan Kent, who picked the ball up in his own half, played a one-two with Glen Kamara and then ran through to score, albeit via a slight deflection off Aleksandar Dragović. Ben Nabouhane's added-time penalty was too little, too late for the home side.
Key stat: Rangers had scored the first goal in their previous five Europa League matches before this game – James Tavernier had been the first scorer in the last three.
Monaco 1-1 Braga (agg: 1-3)
Braga cruised through to the last eight after a comfortable night at Stade Louis II. The Portuguese side were always firm favourites after winning the home leg 2-0, and when Abel Ruiz picked up a loose ball and fired in a swerving 20-metre strike which beat Alexander Nübel after 20 minutes, the tie was over as a contest.
Braga goalkeeper Matheus did make a couple of good saves but was not beaten until the dying seconds when Axel Disasi powered home a header, which ensured a draw on the night but could not prevent Braga taking their place in Friday's draw.
Key stat: Braga ended a run of six consecutive away defeats in the knockout phase of the Europa League.
Leverkusen 0-1 Atalanta (agg: 2-4)
Jeremie Boga's late winner capped a dogged defensive performance in Leverkusen and sent Atalanta into the last eight. The substitute looked to be heading nowhere after collecting the ball in his own half in added time, but he showed Jonathan Tah a clean pair of heels before bursting into the box and driving a finish into the far corner.
Visiting goalkeeper Juan Musso made two vital stops to deny Moussa Diaby when the French international was sent racing clear as the Italian outfit preserved their lead from the first meeting.
Key stat: Atalanta have now reached the last eight of a European competition for the second time in three seasons.
Galatasaray 1-2 Barcelona (agg: 1-2)
The Blaugrana came from behind to deservedly book their place in the quarter-finals. Galatasaray, led by former Barcelona assistant Domènec Torrent, struck the first significant blow of the tie when Marcão dived to head in Alexandru Cicaldau's 29th-minute corner.
The turning point came eight minutes later as Pedri left two Cimbom players sprawling before stroking in the equaliser, and Xavi Hernández's men never looked back. The winner followed early in the second half, with Iñaki Peña's fine double save ultimately in vain as Frenkie de Jong headed across goal for Pierre-Emerick Aubameyang to pounce.
Key stat: Galatasaray are without a win in their last eight Europa League knockout phase matches (D4 L4).
Winners of the ties earn a place in the quarter-final draw at 13:30 CET on Friday. There will also be draws for the semi-finals and, for procedural purposes, the final which takes place at Seville's Ramón Sánchez-Pizjuán Stadium on 18 May.
Lyon 1-1 Porto (agg: 2-1)
Lyon held on to win a captivating tie and reach the quarter-finals of the Europa League for a third time. They doubled their aggregate advantage 13 minutes in when Moussa Dembélé beat the offside trap to slide home, but Porto levelled on the night thanks to a wonderful volley from Pepê – a first goal in UEFA club competition for the Brazilian.
It was end-to-end stuff in the second half, but neither side could find another goal, although Vitinha scuffed a glorious chance to take the contest into extra time deep in stoppage time.
Key stat: Lyon have only failed to score in one of their last 27 Europa League matches.
West Ham 2-0 Sevilla (agg: 2-1)
Andriy Yarmolenko's finish in extra time allowed West Ham to overturn a first-leg deficit and become the first English team to beat Sevilla in the Europa League. Tomáš Souček's towering first-half header from an exquisite Michail Antonio cross opened the scoring, and Alphonse Areola's save denied visiting striker Youssef En-Nesyri.
David Moyes' men were the more threatening in the second half and extra time and were rewarded in the 112th minute when Yassine Bounou parried Pablo Fornals' curling effort, allowing Yarmolenko to dispatch the rebound.
Key stat: The Hammers have won five of the last six UEFA competition ties in which they lost the first leg away.
Eintracht Frankfurt 1-1 Real Betis (agg: 3-2)
Frankfurt snatched a place in the last eight for the second time in four seasons after seeing off Betis in the final seconds of extra time. Holding a 2-1 advantage from the first leg in Seville, the hosts looked comfortable in the first half, and Ansgar Knauff and Filip Kostić struck the woodwork either side of the break.
However, Borja Iglesias popped up in the 90th minute to turn in a cross from Nabil Fekir and send the tie into extra time. With spot kicks looming, a Kostić free-kick bounced into the unguarded net off Betis' Guido Rodríguez to spark wild celebrations.
Key stat: Betis have still never progressed further than the round of 16 in their nine appearances in the UEFA Cup/Europa League.
No away goals rule
There has been a rule change for 2021/22: ties level after the second leg go to extra time and a penalty shoot-out if required, irrespective of the number of away goals a team has scored.