Cristiano Ronaldo scored one of the softest goals of his career as Mourinho's team set up a titanic semi-final confrontation with arch-rivals Barcelona on April 27 and May 3.
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Spurs keeper Heurelho Gomes allowed a long-range Ronaldo shot to bounce out of his hands in the 50th minute and failed to retrieve the ball as it bounced agonisingly over the line at White Hart Lane.
Real will now meet Barcelona four times in an epic 17-day spell, starting with Saturday's top of the table La Liga clash and next week's King's Cup final.
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"The semi-final is a semi-final, anything can happen," said Mourinho who lifted the Champions League trophy with Inter Milan last season and with Porto in 2004.
"We have two matches against Barcelona before the semis and there is no time to think. If Spurs had scored in the first half... it could have been difficult but when Cristiano scored it was all over," the Portuguese told ITV Sport.
Real, 4-0 up from last week's first leg, were never in danger of suffering what would have been the biggest reversal since European club competition began in 1955 as they recorded their first away win in the knockout stages for nine years.
The closest Champions League debutants Spurs came to scoring was when Gareth Bale had a first-half goal ruled out because Luka Modric was offside.
Spurs, at the start, set about their virtually impossible task with Bale and Aaron Lennon outpacing Alvaro Arbeloa and Sergio Ramos at will on the flanks before whipping in balls that put Real under pressure.
One run by Bale, when he blazed past Ramos, brought an astonished look to the face of Mourinho, but it was Lennon who created a good chance after 27 minutes.
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Lennon left Arbeloa in his wake again only for Roman Pavlyuchenko to blast the ball into the upper tier of the stands.
Spurs also had three penalty appeals turned down as they continued to go forward, Italian referee Nicola Rizzoli waving away claims after Bale, Modric and Pavlyuchenko all went down under challenges.
Real, naturally enough, were content to sit back and only gave the home defence one moment of real concern in the first half when Ramos forced Gomes to make a fine save from a header and Emmanuel Adebayor lashed the follow-up wide.
The second half lacked the intensity of the first after Ronaldo's goal
