Milan put their domestic difficulties behind them with a 2-1 victory at Red Star Belgrade to go through 3-1 on aggregate while Liverpool had a nervy last 25 minutes in a 1-1 draw with Maccabi Haifa in neutral Kiev for a 3-2 aggregate.
Benfica thrashed Austria Vienna 3-0 in Lisbon for a 4-1 aggregate, Valencia were similarly impressive in beating another Austrian side, Salzburg 3-0 for 3-1 overall, while Hamburg advanced on the away goals rule after a 1-1 draw at Spanish side Osasuna.
Red Star, also former winners of the European Cup, found Milan too hot to handle despite the passionate support of a passionate 55,000 Belgrade crowd.
Filippo Inzaghi headed Milan into a 29th minute lead and Clarence Seedorf made sure in the 78th before Dusan Djokic got a consolation for the hosts.
Maccabi were forced to play in Ukraine because of the security situation in Israel and Liverpool looked like the home side as they dominated the first half.
Liverpool, the 2005 champions, finally converted a chance in the 54th minute when England striker Peter Crouch scored with a header but Maccabi equalised nine minutes later through Roberto Colautti, the Argentine striker who scored their goal in the first leg.
REINA SAVE
Another goal for the Israelis would have taken the tie into extra time but Liverpool keeper Pepe Reina prevented it with a great late save from Colautti.
Portugal will have three teams in the group stage for the first time after Benfica joined Porto and Sporting in Thursday's draw.
Rui Costa, back from Milan at the club where he began his career as a schoolboy, opened the scoring, Nuno Gomes made it 2-0 before halftime and Armando Petit got the third in the 57th.
Strike duo Fernando Morientes and David Villa turned things round for Valencia with goals after 13 and 32 minutes as Salzburg saw their 1-0 first-leg lead quickly blown away.
One goal for the visitors would have still sent them through but the final word went to Valencia's David Silva.
Osasuna, who held Hamburg 0-0 in the first leg, looked on the verge of going through after Carlos Cuellar put them in front six minutes into the second leg but Hamburg scrambled the decisive away goal through Nigel de Jong 16 minutes from the end.
The rest of the third qualifying round is completed on Wednesday, with the draw for the group stage taking place in Monaco on Thursday evening.
