Dynamo Kiev, with a goal from the "Ronaldo of the East" Andrei Shevchenko 10 minutes after the break, earned a useful 1-1 draw at Real Madrid, who equalised through Yugoslavia's Predrag Mijatovic.
Bayern Munich won the all-German battle against Kaiserslautern 2-0 with goals from Giovane Elber and Stefan Effenberg while Olympiakos gave themselves some hope for the second leg against Juventus when they scored a late penalty in Turin to leave them with a 2-1 deficit.
Mijatovic proved again he is Real Madrid's talisman as he salvaged a point just 12 minutes after Dynamo Kiev looked to have taken charge of the tie.
Mijatovic, whose goal against Juventus last May earned Real their first triumph in the competition for three decades, hit a brilliant equaliser from a free kick after 67 minutes.
Earlier, Shevchenko dealt a severe blow to Real Madrid's hopes of successfully defending their title with a clinically taken goal.
The baby-faced striker, reportedly bound for AC Milan, was left in acres of space by a leaden-footed Real defence.
But his control was superb as he took down the ball before clipping the opener past Bodo Illgner after 55 minutes.
Juventus earned a hollow victory over Olympiakos after being suckered by a Greek penalty in the seventh minute of injury time.
Juventus could have won by a cricket score if their finishing had been up to the mark. Inzaghi could easily have bagged a hat-trick before the striker finally hammered the ball home in the 38th minute. Antonio Conte rifled home the second 10 minutes from the end.
However, Angelo Peruzzi hauled down Alexios Alexandris in a goal-mouth scramble and was booked before Andreas Niniadis, who had only come on at the start of injury-time, stepped up to lash the ball into the right hand corner of the net.
Bayern Munich's win is part of a scintillating run of form and they have a realistic shot at pulling off a rare triple: the European Champions trophy, the Bundesliga and the German Cup.
