Madrid:Two first-half goals by Raul Gonzalez and another by Ruud van Nistelrooy gave Real Madrid a 3-2 victory over Bayern Munich in a first-leg match of the European Champions League's second round on Tuesday. Raul, the competition's all-time leading scorer, struck in the 10th and 28th minutes to give him 56 goals, while van Nistelrooy added another in the 34th. Defender Lucio scored for Bayern in the 23rd, with midfielder Mark van Bommel adding what may be a vital goal in the 88th. Madrid's victory at Santiago Bernabeu Stadium may have eased the pressure on coach Fabio Capello, who reportedly offered to quit on Monday, seven months into his second spell in charge. "Bayern made three important changes, which made the difference. They pushed hard, sending balls into our area and their fresh players made an impact," said Capello, who refused to answer questions about his future. Bayern coach Ottmar Hitzfeld said his team showed "a few loose areas, especially in defence." "We came to win or at least to draw so I can't accept a defeat," Hitzfeld said. "I liked the second half. We had several chances while denying Real Madrid any." The second leg in Munich is set for March 7. Madrid capitalises Nine-time champion Madrid had been struggling for goals all season, especially at home, but this time capitalised early on some poor Bayern defending. Raul scored first, converting when his first touch from van Nistelrooy's ball deflected off goalkeeper Oliver Kahn and landed conveniently to angle into an empty net. Bayern equalised when Willy Sagnol's lofted free kick caught Fabio Cannavaro out of position, allowing Lucio to power a header past goalkeeper Iker Casillas. Lucio also scored against Madrid in the 2002 Champions League final, which the Spanish side won 2-1. Defender Ivan Helguera helped to restore Madrid's lead with a looping header at the far post from David Beckham's corner. Raul nodded the ball over the line. Van Nistelrooy fired Madrid's third goal past Kahn to extend the Spanish side's lead after a Helguera header helped on Beckham's swerving free kick. "Up to now, my team has generally played better second halves, but this time we were better in the first," Capello said. However, Madrid twice nearly added a fourth goal early in the second half when Kahn blocked Gonzalo Higuain's shot and then pushed Beckham's free kick onto the bar. Madrid left back Roberto Carlos, returning after a month on the sidelines with a torn calf muscle, left the field in the 59th with what appeared to be a recurrence of the injury. Bayern then took control, forcing Madrid into some desperate defending. Capello praised Bayern's 60th-minute insertion of Claudio Pizarro for striker Lukas Podolski. "When Pizarro came on, Bayern played its most dangerous soccer," Madrid's coach said. Pizarro headed onto the post in the 67th following a mistake by Casillas. However, Madrid's goalkeeper atoned for his mistake with two diving saves on low shots by Pizarro. Bayern made the breakthrough when Van Bommel, who previously played for Madrid's archrival FC Barcelona, fired a fierce half-volley from the edge of the area to improve the German team's hopes of reaching the quarterfinals.