England striker Danny Welbeck gave Alex Ferguson´s side the lead at the Bernabeu before former Old Trafford star Cristiano Ronaldo levelled later in the first half.[break]
In the night´s other last-16 tie, German champions Borussia Dortmund drew 2-2 at Shakhtar Donetsk in a game overshadowed by a horrifying plane crash at the Ukraine city´s airport which killed five fans.
"It´s very open still," said Ferguson. "We have a big job on our hands but it´s within our grasp.
"This is a difficult place to come but the players have dug in and got a good result. We had great chances."
In a match described by Real Madrid coach Jose Mourinho as the clash the "whole world was waiting for", it was the home side who came close early on with United keeper David De Gea, playing in the city of his birth, pushing a Fabio Coentrao drive onto the post.
But it was United who snatched the lead after 20 minutes when Welbeck shrugged off the attentions of Sergio Ramos to head in a Wayne Rooney corner.
Real were level after half an hour with Ronaldo living up the huge pre-match hype by scoring against his former club.
Ronaldo out-jumped Patrice Evra to send a powerful header off an Angel Di Maria left-wing cross past De Gea.
The Portuguese star´s subdued celebrations reflected the warmth with which he still regards United where he spent six seasons.
De Gea, thriving in the city where he made his name with Atletico, was on hand again early in the second period to deny Di Maria before Japan´s Shinji Kagawa made way for veteran Ryan Giggs making his 150th European appearance.
Robin van Persie than saw a shot saved by Diego Lopez with the ball coming back off the crossbar while, moments later, the Dutchman miscued a close range effort which was cleared off the line by Xabi Alonso.
"Everything is very open for second leg," said Mourinho.
"For them they played very tactically, they play very deep especially in second-half. They were waiting for a set piece to score. Even going there for second leg we can score goals."
Van Persie said that home advantage in the second leg in March does not mean that the tie is over.
"We have a slight advantage but at this kind of level it doesn´t matter if it´s home or away," he said.
In Donetsk, five fans of the Ukraine team, who had flown in for the match, were killed when their Antonov AN-24 plane, arriving from Odessa, was forced into an emergency landing.
There was a minute´s silence before kick-off at the Donbass Arena.
Dortmund, the 1997 European champions, almost snatched an early lead when Mats Hummels headed against the crossbar from a corner.
But it was Shakhtar who took a 30th-minute lead when a Darijo Srna free-kick evaded the Dortmund defence before beating goalkeeper Roman Weidenfeller.
The German champions were level four minutes before the interval when Robert Lewandowski found the target after being set-up by Mario Goetze.
Shakhtar regained the lead after 68 minutes when substitute Douglas Costa scored with a left-foot drive but Dortmund finished on top and Hummels levelled for 2-2 with three minutes left.
"It is important that we are going into the second leg level and a 0-0 would see us through," said Hummels.
"Certainly there were a few dangerous moments in defence, but against a such an attack-minded team you can never avoid this."
Champions League last-16 first leg results on Wednesday:
At Madrid
Real Madrid (ESP) 1 (Cristiano Ronaldo 30) Manchester United (ENG) 1 (Welbeck 20)
Madrid eliminates Atletico, reaches Champions League final
At Donetsk, Ukraine
Shakhtar Donetsk (UKR) 2 (Srna 31, Douglas Costa 68) Borussia Dortmund (GER) 2 (Lewandowski 41, Hummels 87)
Played Tuesday
At Glasgow
Celtic (SCO) 0 Juventus (ITA) 3 (Matri 3, Marchisio 77, Vucinic 83)
At Valencia
Valencia (ESP) 1 (Rami 90) Paris Saint-Germain (FRA) 2 (Lavezzi 10, Pastore 43)