Former UEFA Cup winners Inter Milan, Liverpool and PSV Eindhoven reached the last 16 on Wednesday but Parma and Galatasaray bowed out after being thrashed 3-0 in third round, second leg ties.
Barcelona saw off Denmark's Brondby and fellow former European champions Benfica will also be in Thursday's draw after scraping through on away goals against Rosenborg Trondheim.
Italian soccer needed a tonic after a nationwide fraud probe was launched this week and three-times winners Inter and AS Roma just about delivered it.
Inter battled to a goalless draw against French side Sochaux that sent them through on away goals, though their Italy striker Christian Vieri was sent off four minutes from time after appearing to elbow an opponent.
Parma, UEFA Cup winners in 1995 and 1999, faced an uphill struggle after losing the first leg 1-0 at home to Genclerbirligi and their hopes of rescuing the tie effectively ended when goalkeeper Sebastien Frey was sent off in the 37th minute.
Filip Daems converted the penalty and late goals by Matteo Ferrari, who put through his own net, and Ali Tandogan completed a miserable week for financially troubled Parma.
Roma, second in Serie A, had better luck in turning around their tie against Turkish opponents after trailing 1-0 from the first leg at Gazientepspor, strikes from Brazilian Emerson and Antonio Cassano sending them through.
"You must not underestimate Turkish football," Roma coach Fabio Capello said. "We had to play well to win tonight."
IMPRESSIVE STYLE
Galatasaray, the first Turkish winners of a European trophy when they lifted the UEFA Cup in 2000, were knocked out by Spanish side Villarreal.
Spectacular strikes from Sonny Anderson and midfielders Roger Garcia and Juan Roman Riquelme helped the Spaniards seal a comfortable 5-2 aggregate win.
Luis Garcia and Philip Cocu were on target as in-form Barcelona brushed aside Brondby 2-1 to complete a 3-1 aggregate win, their eighth successive victory in all competitions.
After a 3-2 triumph in the first leg in Spain, Valencia had an easier time against Turkish champions Besiktas, winning 2-0 through goals by Miguel Angel Angulo and Juan Sanchez.
Also in need of a tonic was Liverpool manager Gerard Houllier, who recently received a letter threatening his life if he did not resign.
Early goals from England internationals Steven Gerrard and Michael Owen gave the three-times UEFA Cup winners a perfect start at Levski Sofia and headers from Dietmar Hamann and Sami Hyypia sealed a 4-2 win for a 6-2 aggregate triumph.
"It (the death threat) does not affect my passion for my job," Houllier told reporters. "It doesn't affect my love for the city, my affection for the people of Liverpool and the fans who today were absolutely phenomenal."
Two goals from Shola Ameobi and an Alan Shearer free kick helped Newcastle United to an unconvincing 3-1 victory over Norway's Valerenga, Bobby Robson's side going through 4-2 on aggregate, and Dutch champions PSV Eindhoven also won 3-1 on the night and on aggregate against Perugia.
French hopes of a first triumph in the competition were kept alive by the progress of Olympique Marseille, AJ Auxerre and Girondins Bordeaux.
A goalless draw sent Marseille through courtesy of a 1-0 home victory over Dnipro Dnipropetrovsk in Ukraine last week and Auxerre needed a 72nd-minute Bonaventure Kalou goal at Panathinaikos for a 1-0 aggregate win. Bordeaux crushed Poland's Groclin Grodzisk 4-1 for a 5-1 aggregate success.
Benfica's Nuno Gomez had a mixed night at Rosenborg, scoring the vital away goal in a 2-1 defeat before being sent off and last season's runners-up Celtic completed a 3-1 aggregate victory over Teplice despite losing 1-0 in the Czech Republic.
The draw for the remainder of the competition takes place in Nyon, Switzerland on Thursday (1300 GMT).
