Danny Welbeck netted in the 1-1 draw at the Santiago Bernabeu a fortnight ago to give United a slender advantage ahead of tonight's reverse fixture.
It was the England international, surprisingly preferred to Wayne Rooney in United's attack, who came the closest to adding to the scores in an opening 45 minutes during which the hosts had most of the chances.
The stand-in stopper enjoyed another slice of luck after the half-hour mark.
He clumsily parried a stinging Robin van Persie shot, but made amends by reacting quickly to block Welbeck's follow-up effort.
Cristiano Ronaldo, returning to Old Trafford for the first time since leaving United for Los Blancos in 2009, was rarely involved in Madrid's forward ventures.
When the visitors did threaten, it was neat one-touch passing from Mesut Ozil and Angel Di Maria, who was forced off injured and replaced by Kaka as the interval approached, that set up Gonzalo Higuain.
However, the Argentine's bending shot went wide of the far post, and when he did find the target, David de Gea was on hand to deny him with a smart save from a tight angle.
Madrid must score in the second period or they will be eliminated.