The Spanish giants had the majority of possession and peppered the Red Devils' goal all night, yet could not break the 1-1 deadlock established earlier—giving United a huge advantage heading into the return leg at Old Trafford next week.
The away-goal rule means that Sir Alex Ferguson's men can win by any amount and progress, or even pick up a 0-0 draw and still go through to the quarterfinals.
Which, given the dominance that Madrid have had at the Bernabeu over the years, is a huge result for the English Premier League leaders.
However, as strong as the performance was from the Red Devils in terms of keeping Los Blancos at bay, several areas of improvement are still needed for United. Especially if they plan on winning the second leg at home and progressing through to the next round of the UEFA Champions League.
Jose Mourinho's side are simply too strong and too talented for improvements not to be made by Ferguson, who no doubt knows where his side were lacking.
Here's three tactical and positional changes that United must make in order to win their second leg against Real Madrid in the Champions League round of 16.
Start Tom Cleverley in central midfield
Sir Alex Ferguson opted for a central midfield pairing of Phil Jones and Michael Carrick here that would give United some extra defensive cover against Madrid.
And for the most part, the tactic worked well.
Jones shadowed Cristiano Ronaldo as best as anyone can and Carrick continued to link up into the Red Devils defense to prove that extra bit of support and assistance that the four across the back needed from time to time in this one.
However, Rafael at right back didn't fare so well with the pressure that both Ronaldo and Angel Di Maria put on him throughout the match, and I think, will be lucky to hang on to his starting position when the two clubs meet again.
Jones should be shipped out to right back to cover Ronaldo and shadow him like he did, and Carrick or Jonny Evans can be played in the defensive midfielder's role in the middle of the field to pick up Ronaldo when he drifts inwards.
And with all that defensive focus, it would therefore be worth using someone like Tom Cleverley in the middle of the field to give United some go-forward in attack—this could push Wayne Rooney out of the central midfield role that he played here.
Much like Ryan Giggs did when he came on, the England international Cleverley can provide United with another attacking threat from midfield. Which, in a game where they'll most likely need to score goals, seems like a good thing.
Start Antonio Valencia at left-wing
Shinji Kagawa has been effective against the right lineups this season for Manchester United, but he didn't really find much traction here in this one.
The Japanese international never picked up Di Maria or Ronaldo when he came out on to the right flank, yet he never really gave United much of an attacking presence either, with Van Persie having more success out on the left than Kagawa.
Danny Welbeck justified his selection and seems like a great inclusion again against Madrid—if Valencia is going to start, it will be out on the left. Which, could be a very good thing for both United's attack and defense.
The Ecuadorian obviously offers a great threat going forward, and his ability to run with the ball past defenders will be useful if he ends up isolated like Kagawa was. However, his defensive skills as well—which improve with every passing year—could also be huge in snuffing out Di Maria's runs in from the right flank as well as Ozil's success through the middle of the pitch.
Ronaldo is a problem that isn't going to go away for United, so they need to make sure they can identify the other options for Real Madrid in the second leg.
Antonio Valencia is the best man to make that happen on the wings.
Keep Rio Ferdinand in the starting side
Rio Ferdinand did two things in this one that many people (including myself) thought he wouldn't do—start the match, and have a very strong game.
The England international never really got that high up the pitch in order to allow himself to get beat in behind—which was always the biggest concern with Ferdinand—but even still, he did an excellent job against some quality attacking from Madrid.
One particular tracking of Ronaldo when the Portuguese star appeared played in on goal from the right flank showed that the England international is still very tight when he needs to be, and he wasn't a step behind in this fixture at all.
Ferdinand has done enough to warrant his selection in the second leg—over either Nemanja Vidic or Evans depending on injuries and the like.
Vidic is the logical assumption to put back with Ferdinand, and if that happens, I think we could see Evans push up into that defensive midfielder role ahead of the back four, which could yield some strong defensive success from United.
Essentially three centre-backs in play, a more solid option at right-back and some better attacking options through central midfield and the left wing; the changes would certainly send United well on their way to the quarterfinals of the 2013 UEFA Champions League.
But there's a long way to go before that happens.
The return leg will take place March 5, 2013 at Old Trafford.
What changes do you think United need to make for the second leg?
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