Mauricio Pochettino’s side have taken a significant stride towards reaching the last 16 for the first time in six seasons thanks to a spirited display in which Spurs had to survive sustained spells of pressure but were only breached by Cristiano Ronaldo’s 43rd-minute equaliser from the penalty spot.
Hugo Lloris made a stunning save from Karim Benzema early in the second half before Harry Kane had a glorious chance to win it but he was denied by an equally remarkable stop from Keylor Navas.
The two sides reconvene at Wembley in a fortnight’s time with Spurs holding a slender advantage due to scoring here – effectively an away goal in their head-to-head meetings, separating the two sides otherwise deadlocked on points and goal difference.
Dele Alli’s suspension forced Pochettino into a reshuffle but he still sprang a surprise in his starting line-up.
Fernando Llorente was handed only the second start of his Spurs career – the first came against Barnsley in the Carabao Cup – operating alongside Kane in a 5-3-2 system which also saw Eric Dier revert to centre-back alongside Toby Alderweireld and Davinson Sanchez.
Harry Winks took up a central midfield position with Christian Eriksen to his right and Moussa Sissoko to his left. Spurs needed time to find their feet but Real were determined not to let them have it.
Within five minutes, the home side could have been ahead. Marcelo looped a ball to the back post which Jan Vertonghen allowed to drop. Achraf Hakimi collected and crossed for Ronaldo, who rose above Alderweireld to plant a header against Lloris’ left-hand upright.
Karim Benzema wasted the rebound, driving wide from inside the box, but the warning shots had been fired.
Ronaldo drilled an effort just wide from the edge of the box as Real turned up the pressure but just as it appeared Spurs would wilt, they suddenly began to cause problems.
Kane forced Navas into a smart save as he met Eriksen’s 19th-minute corner with a firm header before the striker left Marcelo and Sergio Ramos for dead with sublime trickery and crossed dangerously for Llorente.
The £12million deadline day signing from Swansea wanted a penalty for Hakimi’s challenge but Polish referee Szymon Marciniak was unmoved.
Spurs had begun to establish themselves, however, and they built on that momentum to take the lead midway through the half. Serge Aurier crossed from the right and Varane, under pressure from kane, turned the ball into his own net.
The 3,917 travelling fans erupted in unbridled joy. Real responded with intent – with Benzema guilty of another bad miss – but forced their way level just before the interval.
Aurier gave the ball away cheaply and then compounded the error by making a rash tackle on Toni Kroos in the box. Contact was minimal but sufficient for Marciniak to award a spot-kick.
Ronaldo duly despatched the opportunity – his 110th Champions League goal from 143 appearances – and Real went into the interval with their tails up.
They should have gone in front nine minutes after the restart. Casemiro crossed from the right and found Benzema, unmarked, three yards out. Lloris did brilliantly to spread himself and keep the header out but Benzema simply had to score.
Lloris had to be alert again a few minutes later to turn another fierce Ronaldo effort over the bar. It briefly threatened to turn into a personal duel as Ronaldo rode beat three Spurs players before unleashing another strike, this time left-footed from long range, which Lloris beat away after flinging to his left.
Yet Lloris would not have a monopoly on outstanding goalkeeping here. On an increasingly rare foray forward, Eriksen fed Llorente who in turn released Kane with a ball threaded through the heart of Real’s defence.
Kane opened his body up and sent it on its way into the far corner but Navas somehow got his fingertips to it to send the ball behind for a corner. Out of nowhere, Spurs were a threat again. Eriksen found space and tried to beat Navas at his near post but was denied.
Pochettino replaced Llorente with Danny Rose – his first Spurs appearance since January 31 – for the final 10 minutes before introducing Heung-Min Son for Sissoko but both sides had to settle for a point. Spurs were unequivocally the happier.