Having fallen in the last 16 in each of the last six years, this was the time for Jose Mourinho to show his Real side are ready to go all the way and, with two goals from Emmanuel Adebayor, as well as strikes from fit-again pair Angel Di Maria and Cristiano Ronaldo, they did just that.
Their English opponents, who had seen off AC Milan in the previous round, went behind in just the fourth minute as Adebayor headed home from a corner and then lost Peter Crouch, who collected two yellow cards in the opening 15 minutes.
Key men Ronaldo and Gareth Bale had both been named in the starting XIs after being pre-match injury doubts, but the visitors suffered a blow before kick-off when Aaron Lennon succumbed to sickness and was replaced by Jermaine Jenas at short notice.
Bale offered brief glimpses of hope for Spurs, but their numerical advantage, and a top-drawer performance from Real's attack, meant they never really looked like grabbing an away goal that would have given them a fighting chance of staying in the tie.
The hosts came out of the blocks at a blistering pace, with Ronaldo dancing past the away defence before powering a fierce shot wide.
Just four minutes and one second had elapsed when Real duly opened the scoring from a Mesut Ozil corner.
Adebayor got in front of Jenas and slipped a header past Gomes.
Luka Modric was at the far post but he could not stop the ball squirming in, leaving Adebayor with the opener against the bitter rivals of his former employers Arsenal.
A late challenge from Crouch on Sergio Ramos deep in Real's half earned him a booking soon after.
Adebayor, buoyed by his early strike, constantly probed the Spurs back four, looking for a quick second while Ozil and Ronaldo also looked dangerous.
Real's cause was helped when Crouch was given his marching orders 15 minutes in for a second booking, this time following a late and needless challenge on Marcelo, again deep inside the hosts' half.
Rafael van der Vaart was pushed up front, but he looked isolated and frustrated, earning a booking for petulantly kicking the ball away as Real prepared to take a free-kick.
It looked like only a matter of time before Real doubled their advantage as Tottenham came under intense pressure.
Ronaldo sneaked in behind the back four and fired a volley at Gomes and the brilliant Marcelo was giving Vedran Corluka a torrid time at right-back.
Bale was unleashed for the first time 28 minutes in, bursting down the left but he had three markers on him instantly.
Spurs had a golden chance to draw level just before the half hour when Bale found Van der Vaart in the box with a flat throw but he was denied by a block from Ricardo Carvalho.
Another glimmer of hope came Spurs' way a minute later when Michael Dawson released Bale down the flank but he drove into the side-netting.
Despite that, Real still looked far more dangerous.
Marcelo fizzed a cross to the back post which Ramos headed just out of Adebayor's reach at the back post.
Modric threaded Bale down the left once more and he looked to have beaten Pepe but the Portuguese player slid in, clipping the Welshman's feet and earning a booking.
Real were adamant they should have had a penalty five minutes before the break when Dawson charged down a volley with his arms raised but the referee waved play on.
Spurs boss Harry Redknapp injected some pace into his attack by replacing Van der Vaart with Jermain Defoe at half-time. The striker looked lively, but Real's ascendancy was shown when Adebayor grabbed his second after angling a header past Heurelho Gomes from Marcelo's cross to make it 2-0.
Only a brilliant tip-over from Gomes prevented Adebayor from netting his third as the hosts laid siege to the away goal.
Gomes was made to pay for punching at a cross when the ball found its way to Di Maria, who unleashed a beautiful 20-yard curler past the Brazilian for the hosts' third after 72 minutes.
Defoe saw yellow for a high foot on Ramos before Adebayor received a standing ovation when he was replaced by Gonzalo Higuain with 15 minutes left.
Real's strength in depth was shown minutes later when £56million forward Kaka came on for Di Maria towards the end, while Corluka limped off to be replaced by Sebastien Bassong.
Mourinho barked orders to his players, urging to find a fourth and Ramos came close to obliging with a drive that whistled just wide.
The killer blow came three minutes from the end though when Ronaldo got the goal his performance deserved, rifling a 20-yard volley past Gomes from Kaka's cross.