Real, who won the European Cup for a record ninth time in Glasgow last season, outclassed their opponents on a night the English side will quickly want to forget.
The Spaniards, superior throughout, will be strong favourites to book a semi-final place against Juventus or Barcelona, but they may yet have cause to regret a 52nd minute reply from Ruud van Nistelrooy.
Van Nistelrooy, United's sole attacking threat, headed in from close range after Iker Casillas had palmed away a Ryan Giggs effort.
The Dutchman's 11th Champions League goal of the campaign, a record for an individual season, gave United a lifeline to take back to Old Trafford in two weeks' time.
Their task will not be made any easier, though, by yellow cards for Gary Neville and Paul Scholes, who will both now be suspended for the return.
Alex Ferguson's side scarcely to deserve to still be in the tie after what was a shambolic display.
History suggests that whoever emerges triumphant from the tie will go on to win the final at Manchester United's Old Trafford in May.
The two sides have had three previous meetings in Europe's premier club competition and each time the winner has gone on to lift the trophy -- Real Madrid in 1956-57, United in 1967-68 and Real again in 1999-2000.
Neither side had the look of champions early on, though, as passes regularly went astray in what was a nervous opening at a simmering Bernabeu, packed to its 75,000 capacity.
United did create a couple of chances, Paul Scholes forcing a low save from Iker Casillas with a snap shot and Ruud van Nistelrooy going just over with an overhead kick, but the opening goal robbed them of every sap of confidence.
There seemed to be little danger when Figo collected a short pass from Zinedine Zidane on the left in the 12th minute and shuffled a couple of steps infield.
The Portuguese midfielder spotted that Fabien Barthez was slightly out of position, however, and sent in a wickedly curling shot that crept in at the far corner past the Frenchman's outstretched hand.
Real should have been awarded a penalty when Wes Brown bundled over Ronaldo in the area on 19 minutes but the home side did not have to wait too much longer for the second.
Zidane was again the provider, slipping a pass through to Raul on the edge of the area. The Spanish international forward fooled Rio Ferdinand with a backward feint and turned to drill a shot in at the near post.
United had one good chance to reduce the arrears when Van Nistelrooy was set clear for a run on goal, but his shot flashed just wide.
Ferguson's side might have been in even worse trouble had Swedish referee Anders Frisk decided that Barthez deserved a red card for clearly handling outside the box.
United were indeed in a deeper mess soon after the restart.
Figo, advancing menacingly down the right once again, cut the ball back for Raul to fire a shot through a crowd of defenders and make it 3-0 to Real with his 43rd Champions League goal.
United were staring at a humiliating defeat but to their credit they tore forward and were rewarded within three minutes when Van Nistelrooy headed in after Giggs had taken a Neville cross and forced a save from Casillas.
Real had several chances to restore their three-goal lead but Roberto Carlos, Raul and Figo all fired wide from good positions as huge gaps appeared in the United defence.
For all their efforts at the other end, United could not get another goal back and had to be content with the glimmer of hope left to them by Van Nistelrooy's goal.
Manchester United manager Alex Ferguson later hailed Raul as the world's best player.
Real had Ronaldo in attack and Figo and Zinedine Zidane in midfield, three of the most expensive players in the world, but Ferguson was most impressed with home-grown Raul.
"I hope he doesn't like travelling," said Ferguson with the second leg at Old Trafford in mind. "Failing that we will stop him entering the country.
"Real buy these big players like Figo, Zidane and Ronaldo but I think the best player in the world is Raul.
"The way they take up positions in midfield was very difficult to handle. We know about Zidane, but Raul was just too much."
Ferguson has every reason to be wary of Raul considering the Spaniard's match-winning display the last time the two sides met at Old Trafford three years ago.
Then, United managed to come away from the Bernabeu with a goalless draw only to lose 3-2 at home, with Raul getting two of the goals.
Ferguson was full of praise for Real but clearly unhappy with his side's defending on the first two goals.
"They mesmerise you at times with their controlled passing," Ferguson said.
"The way they control the midfield is very difficult to handle, with Figo and Zidane opening up the game and Raul dropping into space, but having said that I thought the two goals we gave away were very soft."
