But United old boy Cristiano Ronaldo also left his mark on the last-16 tie with a brilliant equalizing header, which he refused to celebrate in recognition of his time at Old Trafford.
Ronaldo also came close with a dipping 40-yard free-kick, whilst David de Gea needed to produce excellent saves to twice deny Fabio Coentrao and the outstanding Mesut Ozil.
There was certainly enough in Real's performance to suggest United would be unwise to claim they now hold a decisive advantage in this two-legged encounter, which will be settled at Old Trafford on March 5, even if Robin van Persie wasted a golden opportunity to seal victory on the night.
United boss Sir Alex Ferguson had promised the game would not finish goalless and, within five minutes, it became obvious why. With their bewildering movement, Real had the capacity to cut their opponents' defense to shreds.
Rafael in particular had a torrid time as Ronaldo roamed the visitors' defense, with Ozil providing impressive support. Angel Di Maria cut inside from his right-wing station and flashed a shot wide before De Gea brilliantly denied Coentrao with a fingertip save to push the full-back's effort onto the post.
With Van Persie also picking up a needless booking when he shoved his hand into Sergio Ramos' face, it was shaping up into one of those nastily uncomfortable European nights - exactly the type United suffered on their last visit to this impressive arena a decade ago.
This Real Madrid are not unbeatable, though, as their current status as Spain's third best team suggests. And on their first meaningful attack, United got their noses in front. How simple it was, too, as Welbeck shrugged off Ramos' attentions, them climbed to turn home Wayne Rooney's corner from six yards.
Analyzing the match on Sky Sports 2, Mourinho said: "Nothing new. Not a surprising match, not a surprising result. "I think basically (it was) what I was waiting for, which is everything very open for the second leg," said the Real Madrid manager. "As I was thinking, I think this will go to the last minute."
Asked if the meeting had resembled a game of chess, the Portuguese replied: "For them - not for us. They changed their way of play.
"They had the block very, very low in the second half. I think Rio (Ferdinand) and (Jonny) Evans - they didn't put one foot in our own half. They were waiting for a set-piece or a counter-attack. They defended well and the result is open. If you ask me percentages, I don't change one single number - 50/50."
Top scorer for England during 2012, Welbeck's only previous goal for United this season came against Stoke. This was an altogether more memorable addition to the 22-year-old's collection and justification of Ferguson's decision to pick him ahead of more orthodox wide players.
The pity for United was that their lead lasted just 10 minutes. Ronaldo should get the equalizer was no shock at all given his tally of 182 goals in 179 games for the Spanish giants prior to Wednesday night's showdown. The way he hung above Patrice Evra before heading Di Maria's cross past De Gea was reminiscent of the Portugal superstar's goal for United in the 2008 final.
His reaction was subdued. There was no celebration even though he was mobbed by ecstatic team-mates. He emerged from the huddle to wave at the Madrid fans before an almost apologetic hand was waved at the visitors' bench.
Welbeck came agonizingly close to restoring United's lead when he nipped in front of Diego Lopez but touched Van Persie's cross inches wide.
Real carried most of the threat though. And Ozil forced De Gea into a tremendous near-post save as the Red Devils defense was caught out by Xabi Alonso's long ball.
The second period took a bit of time to get going. But Di Maria's shot that De Gea had given up as it whistled wide and Raphael Varane's tangle with Evra that sent the Frenchman flying and had Ferguson off his feet waiting for a free-kick and red card that never came ratcheted it up a notch.
And they had de Gea to thank for not falling behind. He was the only one alive to the danger as Coentrao crept in at the far post to meet Sami Khedira's deep cross, instinctively kicking the ball away from his goal-line.
Throughout all the mayhem, Van Persie had been a peripheral figure. It looked like his moment had arrived 15 minutes from time though when, after Lopez had touched his effort onto a post, the Dutchman found himself on his own inside the box as Michael Carrick headed the ball back in.
As Lopez lunged in desperately, Van Persie tried to volley in, only to mis-hit the shot, allowing Alonso to clear off the line. Khedira nearly made United pay with a snap-shot that brought yet another fine stop out of de Gea before Ronaldo's audacious 40-yard free-kick dipped onto the roof of United's net. It was the visitors who had the last word, though, as Van Persie brought a fingertip save out of Lopez.
Mourinho remained upbeat about his side's chances heading into the Old Trafford rematch on March 5. Asked whether the draw handed the advantage to United, he replied: "No. We can score more than one goal there."
Mourinho added: "They had two big chances in the second half, but chances out of context because we were chasing the game and they were just defending. This is the Champions League and there are two matches, home and away. They did their match and they did it well."