Newcastle maintained their perfect UEFA Cup record on foreign soil this season to take a massive stride towards the quarter-final on a stormy night in Greece.
Goals from Alan Shearer, Laurent Robert and Patrick Kluivert gave Graeme Souness' side a crucial lead as Olympiacos were reduced to nine men before the break with Spanish referee Arturo Ibanez a central figure.
The official sent off defender Grigorios Georgatos for a push on Kieron Dyer with just 13 minutes gone, with Shearer gleefully firing home from the spot for his 16th goal of the season and 189th for the club.
Olympiacos were furious with the decision, although they were back in the game within three minutes when Irish international Andy O'Brien was adjudged to have dragged back Ieroklis Stoltidis and Predrag Djordjevic's penalty levelled it.
Another superb free-kick from Robert put the visitors back in front 11 minutes before the break, but there was further drama when Athanasios Kostoulas was dismissed on 43 minutes for a second bookable offence, and Patrick Kluivert took full advantage with a third goal on 69 minutes.
The victory made it six on the trot for the Magpies and five in succession in Europe, on a night when the home fans lived up to their fearsome reputation by hurling missiles on to the pitch.
The night marked the 80th anniversary of Olympiacos' foundation in the Athens port of Piraeus, and with their fans having being allowed back into the Karaiskakis Stadium after a ban for bad behaviour. Another match will be played behind closed doors on Sunday when rivals AEK Athens come to the stadium.
Home victories over Monaco, Liverpool and Deportivo La Coruna in the Champions League and Sochaux in the previous round of the UEFA Cup, all by the only goal of the game, illustrated the Greek side's prowess on their own turf, but their plans were ripped apart in an astonishing opening 45 minutes.
The Greeks dominated the early exchanges, but their flow was fatally interrupted on 13 minutes when, after Dyer ran on to Amdy Faye's through-ball and saw his shot saved by Antonios Nikopolidis.
The England midfielder was pushed in the back by Georgatos as he tried to head the rebound into the empty net and the visitors had a penalty.
Ibanez pointed immediately to the spot and then, to the fury of the home crowd, produced a red card for the offence. Shearer had to wait for some time for calm to be restored before stepping up to smash the penalty high to the keeper's right for his 25th European goal for the club.
It was the first goal the Greeks had conceded in Europe on their own pitch this season, although it would not be the last.
However, the home side were level within three minutes when, after O'Brien was adjudged to have brought down Stoltidis, whose plunge to the turf was delayed to say the least, Djordjevic obliged from the spot to square it.
Newcastle restored their lead 11 minutes before the break when, after he had been tripped by Gabriel Schurrer 22 yards out, Robert curled another superb free-kick into Nikopolidis' top right corner with the keeper rooted to the spot.
Even with 10 men, Olympiacos continued to threaten with Rivaldo, who was clearly unhappy with the injured ankle which almost ruled him out of the game, pulling the strings, but that situation was to change.
Kostoulas, who had been booked for a 25th-minute foul on Dyer, felled Butt two minutes before the break as the visitors broke from deep inside their own half.
Ibanez initially booked Schurrer, but after consulting one of his assistants, called over Kostoulas and sent him off, sparking angry scenes in the home stands.
Newcastle were revelling in the extra-space their numerical advantage afforded them, but there was still plenty of work to be done when Souness decided to make a double substitution.
Off went Robert and Dyer, two of the quickest men in his armoury, and on came Jermaine Jenas and James Milner, perhaps with Sunday's FA Cup quarter-final clash with Tottenham in mind.
Rivaldo made way for compatriot Giovanni, scorer of a Champions League winner against Newcastle for Barcelona back in 1997, with 25 minutes remaining as boss Dusan Bajevic attempted to salvage something from the game, but the visitors took a massive stride towards the last eight on 69 minutes.
The impressive Butt played a fine ball out to Milner on the left and he carved his way through the home defence before squaring for Kluivert to guide home his 10th goal of the season.
