By John Sinnott
Raul scored twice in the first half
Raul got the better of Bayern keeper Oliver Kahn in a one-on-one encounter, before Lucio's header made it 1-1.
By half-time Real were 3-1 up as Raul scored with header, while Van Nistelrooy volleyed in, with David Beckham setting up both those goals.
Bayern were more cohesive in the second-half and with two minutes left Mark van Bommel fired in a half-volley.
Beckham's delivery at set pieces proved key to the nine-times European Champions' win, with the Bayern defence proving uncertain whenever the ball came into the box.
Given this display Beckham must be wondering why he has spent most of the season on the Real bench and is no longer deemed worthy of a place in the England squad.
Not that Beckham's performance was entirely blemish free.
Sent off on Saturday in a Spanish league match at times against Bayern in the first-half Beckham showed flashes of his temper, notably when he was riled by Van Bommel.
Early in the second half he set Gonzalo Higuain free with a raking diagonal pass before forcing Kahn into a fine save with a dipping free-kick.
Not that the Real defence were altogether comfortable at set-pieces as Fabio Cannavaro failed to pick up Lucio for Bayern's equaliser.
Real might also have done better for Bayern's second goal with Van Bommel punishing their inability to clear their lines.
Real's first goal was created by Van Nistelrooy, the Dutchman passing with the outside of his right foot to bisect the Bayern defence and release Raul.
Kahn got a touch as he came out to challenge Raul, but the rebound fell kindly to the Real striker, who sidefooted into the empty net.
At times Real's defence was equally uncomfortable at set-pieces as Cannavaro failed to pick up Lucio for Bayern's equaliser.
Lucio slipped free of Fifa World Player of Year to guide a header past Iker Casillas from Willy Sagnol's free-kick.
But Real were soon to regain their lead, Raul heading home on the line after Ivan Helguera had nodded Beckham's corner goalward.
Beckham and Helguera played a part in Real's third goal, with the Real defender flicking on the Englishman's free-kick.
And Van Nistelrooy provided the perfect finish, volleying past Kahn from close range.
Bayern tightened up defensively after the break and also improved offensively after Claudio Pizarro came on.
In the closing stages Pizarro's low left-footed shot was superbly saved one-handed by Casillas.
But Casillas could do nothing to stop Van Bommel's powerful shot as the Dutchman arrowed in a half-volley from the edge of the penalty area.
Real Madrid: Casillas, Miguel Torres, Cannavaro, Helguera, Roberto Carlos (Raul Bravo 59), Beckham, Gago, Guti, Raul, Higuain (Robinho 53), Van Nistelrooy.
Subs Not Used: Diego Lopez, Salgado, Emerson, Reyes, Mejia.
Goals: Raul 10, 28, Van Nistelrooy 34.
Bayern Munich: Kahn, Sagnol, Lucio, Van Buyten, Lahm, Van Bommel, Hargreaves, Demichelis (Salihamidzic 46), Schweinsteiger (Scholl 79), Makaay, Podolski (Pizarro 61).
Subs Not Used: Rensing, Gorlitz, Santa Cruz, Ottl.
Booked: Demichelis, Schweinsteiger, Hargreaves.
Goals: Lucio 23, Van Bommel 88.
Att: 80,300.
Ref: Frank De Bleeckere (Belgium).
The first leg of the round of sixteen in the  was completed on Wednesday, with at least one controversial result, and a bag full of ties.  The leg began on Tuesday with four games, and the other four were played the next day, including reigning champions FC Barcelona of Spain.

Champions League logo.