Bodø/Glimt finished off Celtic, while Leicester joined former European champions Marseille and PSV Eindhoven in the UEFA Europa Conference League round of 16.
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Former European champions Marseille and PSV Eindhoven took a step closer to becoming the first winners of the UEFA Europa Conference League with solid victories on Thursday, but there was no way back for Celtic as the Glasgow giants were frozen out at Bodø/Glimt.
Elsewhere, Partizan confirmed their place in Friday's round of 16 draw on a topsy-turvy night for Ricardo Gomes, while Slavia Praha marched into the next stage after a second 3-2 victory against Fenerbahçe.Predictor: How did you get on?
A spectacular James Maddison double helped Leicester secure a comprehensive aggregate victory in Denmark. Harvey Barnes put the Foxes ahead after just two minutes, before the hosts grew in stature and Kasper Schmeichel was forced to deny Stephen Odey in fine fashion.
However, Maddison hit a delightful free-kick and a sweet curling effort in the space of four second-half minutes, before Randers cut the deficit late on, Odey capitalising on a defensive mix-up.
Key stat: Barnes' opener was the earliest goal scored by Leicester in European competition.
Bodø/Glimt's European adventure continues after they finished the job they began so well last week in Glasgow. This time their 2-0 win over Celtic was more workmanlike, with a goal after nine minutes from Ola Solbakken putting them in control before Hugo Vetlesen made sure as he finished off a good team move after the break.
The Scottish side never looked like forcing their way back into the tie and Bodø/Glimt were comfortable winners in Norway.
Key stat: The Norwegian champions have won ten of their 12 European home games this century (D1 L1), including seven out of seven in the UEFA Europa Conference League this season.
Yira Collins Sor scored his first two goals for Slavia as his side secured a second 3-2 win against the Yellow Canaries.
Ivan Schranz volleyed Slavia in front, before Sor raced through to finish off the post. Mert Hakan Yandaş hit a fine curler to give Fenerbahçe hope but Slavia were outstanding after the break, Sor hammering into the roof of the net to make it 3-1 after his side spurned a host of chances. Mërgim Berisha's added-time goal was some consolation for Fenerbahçe.
Key stat: Slavia had 21 shots on goal in this game, and have lost just one of their last 13 European matches in Prague.
A clinical Marseille extended their first-leg advantage over Qarabağ to seal a last-16 spot with minimal fuss. The Azerbaijani hosts came out with intent but having weathered the early storm they were undone as Pape Gueye lashed OM ahead after latching on to a fine Dimitri Payet ball.
The visitors sat deep and protected their buffer as Qarabağ chased tirelessly, Matteo Guendouzi and Konrad De La Fuente finally finishing their hopes late on.
Key stat: Qarabağ were competing in a springtime UEFA knockout tie for the first time in their 18 continental campaigns.
The winners will take their place in Friday's round of 16 draw, where they will be unseeded.
The seeded teams are AZ Alkmaar, Basel, Copenhagen, Feyenoord, Gent, LASK, Rennes and Roma.
The Dutch side endured a slightly nervy finish in Israel but still booked their place. PSV looked home and hosed after Yorbe Vertessen's deflected late goal brought some reward for their dominance, but they were forced to weather an unforeseen storm when Enric Saborit's 91st-minute header found the net.
Second best for much of the evening, Maccabi had gone close at 0-0 when Stipe Perica expertly flicked a shot onto the post soon after the restart.
Key stat: Belgian youngster Vertessen has scored 11 goals for club and country this season.
Ricardo Gomes scored twice and was sent off as dominant Partizan forged on. The hosts' bright start was rewarded when Gomes shrugged off a defender and fired in, and he then headed in from a corner for his 26th goal of the season.
Slobodan Urošević had a header ruled out for offside before Gomes was sent off for simulation after going down in the area. Adam Hložek turned in a late consolation for Sparta against the ten men.
Key stat: Partizan have not progressed beyond the last 16 of a UEFA competition since 1989/90, when they were knocked out of the European Cup Winners' Cup quarter-finals by Dinamo Bucureşti.
Alexandros Paschalakis's save from Max Meyer proved crucial as PAOK made it through. Meyer took the first penalty of the shoot-out for his side after the tie ended level, but was denied by the home keeper, and PAOK then converted all five of their penalties to progress.
PAOK grabbed the lead on the night when Andrija Živković prodded in from close range, and Vieirinha put them ahead on aggregate with a stunning long-range effort. However the visitors forced extra time when Meyer teed up fellow substitute Daniel Høegh to score with a header.
Key stat: PAOK have won a UEFA competition penalty shoot-out for the first time, having lost on four previous occasions.
Former Rapid Wien trainee Adrian Grbić landed the first blow early on, racing on to Eli Dasa’s fine, weighted pass to cancel out the visitors' first-leg advantage. Dasa delivered again for the second on 19 minutes, Matúš Bero chesting down his high ball before finishing low to put the hosts ahead in the tie.
Vitesse had chances to settle the game after the break; Dasa had a shot blocked and Maximilian Wittek skidded an effort against the post, but Rapid were unable to exploit their hosts' nerves.
Key stat: Vitesse came into this match having not won in six games (D1 L5), conceding 19 goals in the process.