Benfica came from behind to thrash PAOK 4-1 and book a place in the Champions League group stage alongside PSV and Red Star Belgrade – the latter stunning Red Bull Salzburg with a remarkable fightback to prevail on away goals.
Locked at 1-1 after a disappointing first leg in Lisbon, the Portuguese giant fell behind to PAOK striker Aleksandar Prijovic's close-range finish from Mauricio's pass.
Visiting skipper Jardel powered home the equaliser from a 20th minute corner, six minutes before Eduardo Salvio converted the first of two penalties on the night after Alexandros Paschalakis' foul on Franco Cervi.
Benfica goalkeeper Odisseas Vlachodimos saved brilliantly from Leo Matos – later sent off for a second booking - and Pizzi piled the misery onto PAOK by clipping home a fine 39th-minute finish from the edge of the penalty area.
Salvio's second spot kick came after Fernando Varela was adjudged to have impeded Jardel at a corner, although the home side continued to battle valiantly against the inevitable and Prijovic was only denied a brace by the crossbar.
The result means Benfica take their place among the second seeds for Friday's (AEST) draw – a superior coefficient to Liverpool meaning the Premier League side will now reside in pot three.
Salzburg looked set to be joining such European luminaries in the competition proper when Munas Dabbur scored a quickfire brace either side of half-time to give them a 2-0 lead on the night and overall against Red Star, his second coming after Vujadin Savic fouled Hannes Wolf in the box.
But Ben Nabouhane converted Milos Degenek's right-wing cross at the back post in the 65th minute and a looping header from the Australia international 70 seconds later set up a 2-2 draw and an away goals triumph that Red Star sealed by seeing out a frantic late onslaught.
The full-time whistle prompted a delirious pitch invasion from the travelling supporters, with UEFA likely to take a dim view.
PSV needed late drama to see off BATE 3-2 through substitute Donyell Malen last week but they were a cut above their opponents in Eindhoven, coasting to a 3-0 win.
Captain Luuk de Jong was influential as the attacking focal point, flicking on for Steven Bergwijn's 14th-minute opener before planting home a fine header from Jorrit Hendrix's 36th-minute cross.
Livewire Mexico winger Hirving Lozano struck the bar with an early free-kick and was a constant menace, sealing an emphatic triumph in style after the hour with a right-footed effort beyond goalkeeper Denis Scherbitski.