Danny Welbeck opened the scoring and, although Ronaldo netted a first-half equaliser, that is how it stayed to set up a fascinating second leg.
Real began the brighter and there was a warning for Sir Alex Ferguson's side when David De Gea tipped a Fabio Coentrao effort onto the far post early on.
But it was United who opened the scoring on 20 minutes after Shinji Kagawa was a little fortunate to be awarded a corner following a challenge with Sergio Ramos.
Wayne Rooney swung the subsequent set-piece in from the left and Welbeck did well to pull back from the goal-line before nodding expertly past Diego Lopez.
That left the Bernabeu stunned but, just as the visitors were growing in confidence, there was a riposte from a familiar figure on the half-hour mark.
Angel Di Maria's delivery from the left was met by Ronaldo, who seemed to hang in the air before expertly heading past De Gea.
Real twice went close after the interval through Di Maria before Raphael Varane got the benefit of the doubt for a challenge on Patrice Evra when the United skipper looked to be clean through on goal.
Jose Mourinho's side continued to dominate the ball and De Gea saved well with his feet from Coentrao on the hour mark.
But United remained a threat on the break and Van Persie had a double chance to put his team in front only to see his first shot hit the woodwork and the second cleared off the line by Xabi Alonso.
Despite heavy pressure from the home side, it was Van Persie who forced the final chance of the game as his left-footed effort was saved well by Lopez in injury time.
But a series of conservative substitutions from both managers helped ensure there would be no winner on the night and it sets up an intriguing second leg at Old Trafford in three weeks' time.
"There were a lot of incidents in the match," Sir Alex Ferguson told Sky Sports. "Chances at both ends. David de Gea has made three or four fantastic saves but we have missed some good chances ourselves.
"In all we've created a lot of chances in the match and [played] some good attacking football at times but not had the possession we should have had. I think they won the possession without question.
"But they're at home, it's a difficult place to come to and we're pleased with a result that takes us back to Old Trafford with a great chance."
Jose Mourinho also believes the tie is wide open and said: "It was not a surprise the match or the result. I think it was basically what I was waiting for which was everything open, very open for the second leg. I think this will go to the last minute.
"If you ask me the percentage, I don't change one single number, it's 50/50. We can score more than one goal there."
|Real Madrid||Team Statistics||Manchester United|
|1||1st Half Goals||1|
|8||Shots on Target||6|
|11||Shots off Target||3|
|55.5||1st Half Poss.||44.5|
|65.1||2nd Half Poss.||34.9|