Kemar Roofe's winner sent Rangers into the Europa League last 16 with a 3-2 victory at Real Betis Thursday, while Joao Pedro's late strike helped Brighton and Hove Albion sink Marseille.
Rangers, runners-up in the competition two seasons ago, were heading out of the tournament and into the Europa Conference League with the game level 12 minutes from time and Sparta Prague on their way to a 3-1 victory at Aris.
But after a corner was twice not cleared, Roofe bundled the ball home from three yards out to fire Rangers from third to first in Group C.
The Scottish giants had twice led in the first half through Abdallah Sima and Cyriel Dessers, but Juan Miranda and Ayoze Perez both equalized for Betis.
Rangers held on in a frantic finale to inflict a first home defeat of the season on Betis, who had to settle for a Conference League play-off spot.
Brighton avoided a Europa League knock-out round play-off in February with a tense 1-0 home win over Marseille in Group B.
Both teams had already secured top-two finishes, but the Seagulls needed a win to usurp OM at the top of the standings.
The Premier League side struggled to break down their visitors for long periods, but Pedro showed neat footwork in the box before drilling the ball into the top corner in the 88th minute to score his sixth goal in as many Europa League matches this season.
West Ham United made it a clean sweep for British teams, finishing top of their group as Mohammed Kudus and Edson Alvarez scored in a 2-0 win over Freiburg, who finished second in Group A.
Earlier, a youthful Liverpool side lost 2-1 at Union Saint-Gilloise in their final group game.
Liverpool manager Jurgen Klopp rang the changes with his team already secure as Group E winners and with an eye on the weekend's Premier League game against rivals Manchester United, starting six players aged 20 or younger.
Saint-Gilloise, who needed a victory to keep alive their hopes of pipping Toulouse to second place, took the lead through Mohamed Amoura before Jarell Quansah hit back for Liverpool.
Cameron Puertas restored the hosts' advantage two minutes before half-time with a low strike which beat Caoimhin Kelleher at his near post.
Klopp threw on Joe Gomez, Ryan Gravenberch and Darwin Nunez in the second half, but Saint-Gilloise held on for a famous win, although the Belgians dropped into the Europa Conference League play-off round after Toulouse beat LASK Linz 2-1 in the group's other game to finish second.
Dani Parejo scored a late winner as Villarreal took top spot in Group F and direct qualification for the last 16 with a 3-2 victory at Rennes.
Lorenz Assignon hammered home in the 12th minute of injury time to seemingly send Rennes back to the group summit, but his goal was ruled out by Video Assistant Referee and scuffles broke out after the final whistle.
VAR intervened because Enzo Le Fee had collected the ball himself after his own free-kick had struck the woodwork in the build-up.
"I also learned (this rule) at that time to be very honest," Rennes coach Julian Stephan said.
"I knew it was the case from the penalty spot but I didn't think it could exist from a free kick."
The Ligue 1 club only needed to avoid defeat to finish first, but instead will have to face a team dropping out of the Champions League in the play-off.
Azeri club Qarabag finished second in Group H courtesy of a 2-1 success against Haecken.
They were a distant eight points adrift of group winners Bayer Leverkusen, though, as the Bundesliga leaders extended their unbeaten start to the season to 23 matches in all competitions by thrashing Molde 5-1.
Jose Mourinho's Roma had to settle for a knock-out play-off berth despite beating Sheriff Tiraspol 3-0 as Slavia Prague thrashed Servette 4-0 to finish first in Group G.
RESULTS
Olympiakos 5 (Kaabi 21, Podence 40, 42, Ilic 46-og, El-Arabi 67) Backa Topola 2 (Djakovac 48, Cirkovic 60)
West Ham 2 (Kudus 14, Alvarez 42) Freiburg 0
Ajax 3 (Akpom 5, 56, Taylor 20) AEK Athens 1 (Garcia 11)
Brighton 1 (Pedro 88) Marseille 0
Aris Limassol 1 (Bengtsson 84) Sparta Prague 3 (Kuchta 4, Birmancevic 11, 45+1)
Betis 2 (Miranda 14, Gutierrez 37) Rangers 3 (Sima 10, Dessers 20, Roofe 78)
Rakow Czestochowa 0 Atalanta 4 (Muriel 14, 72, Bonfanti 26, De Ketelaere 90+2)
Sporting 3 (Gyokeres 39, Inacio 60, 70) Sturm Graz 0
LASK 1 (Ljubicic 61) Toulouse 2 (Dallinga 54, Suazo 83)
Union St Gilloise 2 (Amoura 32, Puertas 43) Liverpool 1 (Quansah 39)
Panathinaikos 1 (Ioannidis 89) Maccabi Haifa 2 (David 20, Chery 74)
Rennes 2 (Assignon 37, Blas 79) Villarreal 3 (Gerard 36-P, Akhomach 62, Parejo 80)
Roma 3 (Lukaku 11, Belotti 32, Pisilli 90+3) Sheriff Tiraspol 0
Slavia Prague 4 (Doudera 15, Schranz 25, Chytil 30, 45+1) Servette 0
Leverkusen 5 (Schick 6, Tapsoba 22, Ellingsen 25-og, Hlozek 60, Mbamba 70) Molde 1 (Kitolano 75)
Qarabag 2 (Andrado 1, Benzia 45+3) Haecken 1 (Guseynov 90+4-og)
