Real Madrid broke through thanks to a gem by Vinicius Junior following a few attempts and strong saves, but Benfica contained the damage all in all.
Match Replays
Monaco jumped to an early two-nil lead at home propelled by Balogun, but PSG didn't panic and rallied back, also benefitting from an early red card.
After a back-and-forth in the early going, Galatasaray ran rampant after a Juventus player was expelled, piling on five goals on the opponents.
Newcastle United just need to finish the job in the return leg, as they came out guns blazing and cruised to a six-to-one triumph last week.
Bodø/Glimt produced a surprising 3-1 result in the first leg after two second-half goals, something Inter will try to overcome in their return home.
Bayer Leverkusen built a comfortable advantage heading into the second tie thanks to a quick brace by Schick midway through the second half in Greece.
Atlético Madrid scored twice in the first half, and then again after Club Brugge came back, but their foes refused to go down, leveling the tilt late.
Olympiacos moved on by sweeping their last three matches and closing with just one point fewer than Bayer Leverkusen, which have been steadier.
Club Brugge muscled their way into the top 24 by winning their last two matches. Atlético Madrid paid the price for a slow start and a so-so ending.
Bodø/Glimt soared down the stretch thanks to a seven-point haul in the last three tilts. Inter won five times but also lost to three contenders.
Qarabağ FK treaded water for a while after coming out of the gate hot, but it was enough to advance. Newcastle United finished behind the heavyweights.
Benfica conquered the last playoff berth in the most dramatic fashion, thanks to a last-gasp goal by their goalkeeper Trubin against Real Madrid.