The Greek side's 80th birthday celebrations turned sour at the Karaiskakis stadium in a volatile second knockout round, first leg clash which Newcastle won 3-1. Olympiakos had two players sent off in the first half while Spanish referee Arturo Ibanez awarded a penalty to each side.
Portugal's Sporting and Dutch side AZ Alkmaar chalked up impressive away wins while former winners Parma had eight players booked but held Sevilla to a 0-0 draw in Spain.
Cup favourites Villarreal, beaten by Valencia in the semis last season, will have to wait until Wednesday to play their first leg in Romania against Steaua Bucharest. Heavy snow in the Romanian capital forced the game to be postponed.
Newcastle's passage to victory in Athens was made easier after the Greek league leaders were reduced to nine men, Grigoris Georgatos and Athanasios Kostoulas dismissed in the opening 45 minutes.
Georgatos was sent off for a seemingly innocuous challenge on Kieron Dyer as the England midfielder looked to follow up his own shot on 12 minutes.
Alan Shearer gave Greek international keeper Antonis Nikopolidis no chance from the spot, but the lead lasted just three minutes before Andy O'Brien was penalised for a shirt pull and Serbian Predrag Djordjevic made it 1-1.
Shearer had a header cleared off the line but the Premier League side scored again on 33 minutes, Frenchman Lauren Robert curling home a free kick.
The howls of derision at the Georgios Karaiskakis stadium grew louder just before halftime when Kostoulas was shown a second yellow card, leaving Olympiakos to play the second half with nine men.
They held out until 68 minutes when Dutch striker Patrick Kluivert converted a cross from James Milner to give Newcastle breathing space for the second leg.
"Who can say what the result would have been if it had stayed 11 against 11? All I can say is that we have put ourselves in a very strong position for the return leg although nothing has been decided," said Newcastle manager Graeme Souness.
"I have been in professional football for 37 years and I know that it's not over until it's over."
Sporting, who will host the final at their Alvalade stadium in Lisbon on May 18, were three goals up and cruising to a decisive win at the Riverside against Middlesbrough before two late goals gave the Premier League side hope for the return leg.
Goals in a 16-minute spell in the second half from Pedro Barbosa, Brazilian Liedson and Cameroonian Rudolph Douala put the Portuguese side in control. But Joseph Desire Job scored with an acrobatic bicycle kick 11 minutes from time and then Chris Riggott smashed in to peg Sporting back to 3-2.
AZ Alkmaar did what Barcelona and Celtic could not do in the Champions League this season by defeating Shakhtar Donetsk in Ukraine.
The Dutch side pulled off a fine 3-1 win with goals from Robin Nelisse, Joris Mathijsen and Kenneth Perez, who scored a late penalty.
Alkmaar keeper Henk Timmer had made a fine diving save on the half-hour to keep out Darijo Srna's penalty before Brazilian Matuzalem equalised in first-half stoppage time.
Dutch referee Rene Timmink showed 11 yellow cards, eight of them to Parma players, as the Serie A strugglers drew 0-0 against Sevilla thanks to an inspired display from French goalkeeper Sebastien Frey.
Frey made a series of fine saves and Parma rode their luck late on when Jesus Navas slammed a shot against the woodwork.
AJ Auxerre drew first blood in the all-French tie with Lille, a goal seconds before halftime from striker Kanga Akale earning the away side a 1-0 victory.
Brazilian forward Savio grabbed a valuable away goal as Real Zaragoza fought back from a goal down to hold Austria Vienna to a 1-1 draw at their Ernst Happel stadium.
Savio smashed home at the far post after running on to a neat through ball from midfielder Fernando Soriano 16 minutes from time. Vienna, who defeated Zaragoza 1-0 at home in the group stage, went ahead in the first half through Norwegian striker Siggi Rushfeldt's fine volley.
A late penalty converted by Ivan Tomic earned Partizan Belgrade a 1-1 draw at home to CSKA Moscow after Yevgeny Aldonin had given the Russians the lead after 18 minutes.