Cristiano Ronaldo struck in the 75th minute to deny Derby a sensational draw - and send Manchester United top thanks to Arsenal's draw with Middlesbrough.
Ronaldo was United's main threat throughout the game
Wayne Rooney crossed for Ronaldo to volley home and spare United's blushes.
Ronaldo hit the post in the first half but United had debutant keeper Ben Foster to thank for twice keeping out Kenny Miller just before the break.
After scoring the goal, Ronaldo skipped clean through, only to be denied by former United team-mate Roy Carroll.
Another goal would have been harsh on Derby, who reacted to a 6-1 drubbing by Chelsea with a performance of admirable resilience against the league's top scorers.
United, meanwhile, were hoping to bounce back in style after going out of the FA Cup to Portsmouth - a match in which they spurned numerous chances.
But for 75 minutes, it looked like it would be a recurring nightmare at Pride Park.
They carved out their first good chance after only 59 seconds when Ryan Giggs headed over Ji-Sung Park's cross and went on to dominate the first half-hour.
Ronaldo, playing alongside Rooney up front, hit the post from 12 yards before curling a shot with the outside of his right foot, which keeper Carroll did well to claw away with his fingertips.
Foster did not have a save to make in that period, although a couple of scuffed kicks were perhaps evidence of his debut-day nerves.
But the keeper had a chance to show his class when Derby twice threatened to take a sensational lead against the champions through Miller.
Foster first dived to his left to claw away Miller's volley from an Eddie Lewis cross and then went the same way to stop the striker curling in a shot after Rob Earnshaw's through-ball.
Ronaldo continued to be United's main threat but the Portugal international made no attempt to hide his growing frustration as the ball refused to go into the net.
Carroll saved an audacious 40-yard free-kick, then a header and then another set-piece before Ronaldo lashed a shot into the side netting - prompting him to scream skywards.
But the breakthrough finally came when Rooney muscled his way down the left before crossing for Ronaldo, who did well to steer his volley home with the ball at a difficult height.
Ronaldo's fervent reaction said it all, his goal putting United above Arsenal - who later could only manage a draw at home to Middlesbrough.
Derby boss Paul Jewell
"No one likes losing games but the way we lost is acceptable. I want that sort of performance to be the norm rather than the exception.
"I'm pleased the players put in a shift for the supporters.
"We were never going to be able to out-football them but we matched them for workrate and endeavour."
Manchester United assistant boss Carlos Queiroz
"After their 6-1 defeat against Chelsea they regrouped very well. To tell the truth we didn't expect they could be so strong.
"It was very difficult after we missed so many chances at the beginning. We didn't score and step by step, Derby started to believe.
"But we kept fighting in the second half and got the result we expected."
Derby: Carroll, Edworthy (Todd 55), Leacock, Moore, McEveley, Sterjovski (Robert 83), Savage, Jones, Lewis, Miller, Earnshaw (Villa 77).
Subs Not Used: Price, Ghaly.
Booked: Moore, Jones, Savage, McEveley.
Man Utd: Foster, O'Shea, Brown, Vidic, Evra, Park (Saha 62), Scholes (Carrick 62), Anderson (Fletcher 74), Giggs, Ronaldo, Rooney.
Subs Not Used: Heaton, Hargreaves.
Goals: Ronaldo 76.
Referee: Phil Dowd (Staffordshire).
BBC Sport Player Rater man of the match: Manchester United's Cristiano Ronaldo on 7.93 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.