A quickfire double from captain Raul and a well-taken header by new signing Robinho allowed 10-man Real to fight back from a goal down to record their first victory in three league outings which pushed them into fifth place in the Primera Liga, three points behind leaders Celta Vigo and a point ahead of arch-rivals Barcelona.
Woodgate said: "I just can't believe I got sent off and scored an own goal on my debut - but that's life. I went to try to block the ball and it just skimmed off my head. But I have had worse things happen to me than this and I know I will come back strong.
"I got sent off but I didn't think the second yellow card was justified. But it's the ref's decision and there's nothing I can do about that. That's not the way that I dreamed my debut would be. I am in shock but I have to thank the fans because of the way they responded to me. They've waited a long time to see me play and they must not know what to think, but they have tried to lift me after the own goal and then when I was walking off the pitch they clapped me. That meant to a lot to me. At least things can only get better."
Real showed little sign of improvement in the first period as they struggled to keep control of the ball and were hurried in attack. Robinho managed an isolated shot on goal when he drilled a powerful strike against the post from outside the area after a neat back-heel from Raul in the seventh minute. But without the injured Zinedine Zidane and with Thomas Gravesen and Pablo Garcia occupying the centre of midfield, Real lacked ideas and quickly surrendered the initiative to the visitors.
Things went from bad to worse midway through the half. The injury-plagued Woodgate, playing his first competitive match in 17 months, tried to clear a dangerous cross from striker Joseba Etxeberria with a diving header but only succeeded in diverting the ball into his own net to give Bilbao the lead.
The former Newcastle United defender was lucky to stay on the pitch when he clattered into Carlos Gurpegi before the break, earning a yellow card.
Coach Wanderley Luxemburgo tried to solve his team's problems by sending Guti on in place of Gravesen at half-time and Real looked a different side.
David Beckham whipped in a free kick from the left in the 53rd minute and Robinho headed in at the near post. Robinho's fellow Brazilian, Ronaldo, set up Raul for his first goal 12 minutes later, before the unfortunate Woodgate received his marching orders after he picked up a second booking for a foul on Etxeberria.
Raul made certain of Real's win when he met a 69th-minute corner from Beckham with an expert glancing header that spun over the goalkeeper and into the net.
Real Madrid: Casillas; Salgado, Woodgate, Pavon, Roberto Carlos; Beckham, Gravesen (Guti, 46), Garcia, Raul (De la Red, 86) ; Robinho, Ronaldo (Bravo, 69). Substitutes not used: Cobena (gk), Diogo, Mejia, Balboa
Athletic Bilbao: Aranzubia, Exposito, Prieto, Casas; Ibon, Tiko, Gurpegi (Iraola, 72), Lacruz, Orbaiz; Yeste (Llorente 69), Etxeberria. Substitutes not used: Etxebarrieta (gk), Guerrero, Gonzalez, Murillo, Tarantino
Goals: Real Madrid: Robinho (52), Raul (66), Raul (68). Athletic Bilbao: Woodgate (24, og). Red card: Woodgate 67. Attendance: 70,000
Referee: A. Undiano MallencoReuse content