A headed brace from Togo striker Emmanuel Adebayor and late goals from Angel di Maria and Cristiano Ronaldo put Tottenham to the sword in Madrid's fifth straight home win in Europe and a four-goal lead gives Tottenham a mountain to climb in the second leg at White Hart Lane on April 13.
Tottenham, who last reached a European Cup semi-final back in 1962, were left to rue the early sending off of striker Peter Crouch on 15 minutes for a late lunge as Real made the ten men pay.
"I haven't seen a replay of the tackle," said Tottenham coach Harry Redknapp. "He already has a yellow card and he shouldn't take the chance of getting a red card. I am disappointed.
"It is going to be difficult to turn around. Trailing 4-0 to Real Madrid is very difficult and we have a mountain to climb no doubt about that, but we will give our all at White Hart Lane."
Real coach Jose Mourinho had seen his 150-match nine-year unbeaten home league record come to an end on Saturday with a 1-0 loss against Sporting Gijon, however, his team responded with a victory that puts the nine-time champions in the driving seat to reach the last four.
And Mourinho admitted that Crouch's sending off had made Tottenham's task almost impossible.
"I know at his level, 11 against 10, it's almost impossible," he said on Sky Sports Two.
"It's just a question of the team with 11 keeping concentrated and we did that in the second half, not in the first half but in the second half we did that.
"For a team with 10 men for such a long time is an impossible mission
"I feel sorry because with 11 against 11 the match would be much better."
But Mourinho believes Tottenham are still very much in the tie.
"I know English football well, I know the English mentality. In another culture, yes, but with the English concept of football it's not over."
Mourinho, who won the Champions League with Inter Milan on this ground last May, said he would have to take a risk on Portuguese star Ronaldo, who was struggling with a hamstring complaint, and he felt the gamble was worth it as the world's most expensive player started.
Brazilian left back Marcelo also came back from injury with Adebayor starting as a lone striker.
Redknapp welcomed Welsh winger Gareth Bale overcoming a niggling hamstring to start, while experienced French centre-back Willam Gallas was passed fit.
Dutch midfielder Rafael van der Vaart started against his old club, but Redknapp had to draft in Jermaine Jenas for Aaron Lennon at the last minute.
The Bernabeu home crowd were nervous after the shock loss to Gijon, but the hosts got off to the perfect start scoring after just four minutes.
A corner from the right found Adebayor in the penalty area and the striker planted a header goal wards and the unfortunate Luka Modric could not keep the effort out as it went between his legs.
It was a setback for the visitors, who were then reduced to ten men on 15 minutes with Crouch's rash lunge on Marcelo earning him a second caution.
Real dominated possession but a half chance from Ronaldo was all they had to show for their extra man.
Bale had been quiet but sparked into life in the 28th minute with his gigantic throw catching Real off guard but van der Vaart could not get a shot off.
Bale then powered down the left and homed in on goal but his shot went into the side netting.
Adebayor, well known to the Spurs fans from his Arsenal days, was inches away from heading in his second goal on 32 minutes but was centimetres away from converting Sergio Ramos' unorthodox headed cross.
Portuguese centre-back Pepe was booked for hacking down Bale close to half-time and will now the miss return leg.
Van der Vaart made way for striker Jermain Defoe in the second half in a brave move from Redknapp.
Ronaldo, shooting from everywhere, drilled a left-footed shot wide of the post early in the second half to sound out a warning.
On 57 minutes Real got the second goal they craved with a corner finding Marcelo who crossed and Adebayor was again unmarked to direct a header into the corner.
Adebayor almost got a hat-trick with another header before Argentine di Maria netted on 72 minutes cutting inside before bending a terrific shot into the corner with his left foot.
Ronaldo made it four in the closing minutes with a volley although goalkeeper Heurelho Gomes should have done better.
"We have to take advantage of this lead because anything can happen and we can't underestimate Tottenham," said Ronaldo.
"Regardless of the fact that we were playing against ten men the team played well. It was tough going in the first half but we improved a lot in the second half."