Real, UEFA Cup winners in 1985 and 1986, scored a last-minute goal to beat Danish part-timers Odense 3-2 on Tuesday night away from home. Bilbao beat Italians Parma 1-0 at home and Deportivo won at home, also 1-0, against German league leaders Borussia Dortmund.
But Spain's ambition of winning the UEFA Cup for the first time since Real's victory in 1986 will be severely tested -- not least by Bayer Leverkusen of Germany and Lazio of Italy who virtually ensured their places in the last eight in March with important away wins.
Three more first leg matches are scheduled for Thursday night: Admira Wacker vs. Juventus; Nantes vs. Sion and Eintracht Frankfurt against Napoli.
Real Madrid 3, Odense 2. Real Madrid went to Odense, the birthplace of Hans Christian Andersen, but there was no fairy-tale ending for the home side as a last minute goal from Danish international Michael Laudrup gave Real a 3-2 victory.
"That's soccer. I'm a professional and even against a Danish side I must do my best," said Laudrup afterwards.
Odense's part-timers led 1-0 through Michael Schjoenberg but trailed 2-1 after Real strikers Ivan Zamorano and Jose Amavisca scored in the 67th and 69th minutes.
Substitute Jesper Hjorth scored a 79th minute equalizer just six minutes after coming on before Real, the UEFA Cup winners of 1985 and 1986, clinched victory.
Athletic Bilbao 1, Parma 0. Athletic Bilbao, who beat Newcastle of England in the previous round on away goals after trailing 3-0 at one stage of that tie, needed all the patience they showed then to break down the stubborn resistance of Italians Parma to win 1-0 at home.
The only goal came three minutes after halftime when Jose Ziganda deftly headed home a near post cross from Julen Guerrero. It was the first goal Parma had conceded in the competition.
Deportivo 1, Borussia Dortmund 0. Deportivo's goal that sank Dortmund was one made in Brazil. The move was started by Donato Gama da Silva, Brazilian-born but now a Spanish national, and ended with Brazil's World Cup striker Bebeto controlling the ball on his chest before firing home a spectacular volley off the underside of the Dortmund crossbar.
Bayer Leverkusen 4, Katowice 1. The most dramatic goal-scoring burst came in Poland where Leverkusen strikers Ulf Kirsten and Hans-Peter Lehnhoff scored three times in 14 minutes against Katowice. A second Lehnhoff goal in the second half killed off the Poles.
Lazio 2, Trabonzspor 1. Lazio also enjoyed a scoring burst in Turkey with Roberto Rambaudi (59th) and defender Paolo Negro (61st) seeing off Trabzonspor.
Unal Karaman pulled one back for the Turks who now have a huge job on their hands if they wish to repeat their giant-killing performance of round two when they knocked out former European champions Aston Villa of England.
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