A superb Kris Commons strike was the least Derby deserved for a thoroughly terrific and at times inspired display that must have impressed the new manager who watched from the director's box.
United were well below par but this should not detract from what was Derby's best performance of what has been a difficult season.
The World Club champions will still be favourites to go through to the Carling Cup Final in the second leg at Old Trafford but they will have to do a lot better than they did at Pride Park on a cold, misty night.
Derby keeper Roy Carroll was only tested once and that was in the first minute of stoppage time when substitute Michael Carrick headed a free-kick straight at him.
Apart from that, United were restricted to some wayward long range shooting and a couple of Cristiano Ronaldo free-kicks, one of which went only inches wide 12 minutes from the end.
The fact that United had so few openings was down to an outstanding performance at centre-back by Andy Todd, who was recalled after a loan spell at Northampton, and another towering display in midfield from teenager Miles Addison.
Derby slowed United down at every opportunity and denied the Premier League champions the chance to get into any kind of rhythm.
The home side had already gone close through Steve Davies before they went in front on the half hour when Mile Sterjovski played the ball inside to Commons who took a touch before unleashing a 25-yard left foot shot that arrowed into the bottom left corner.
The expected introduction of Ronaldo and Wayne Rooney early in the second half failed to produce a transformation in United who continued to struggle.
Although Ronaldo went agonisingly close with that free-kick it was Derby who almost scored a second ten minutes from the end when Commons had a shot parried by Tomasz Kuszczak and Rob Hulse put the rebound over the bar with the goalkeeper stranded.