Burnley were last in the top flight in 1976 and they celebrated their first home game with a sensational win over last season's Champions.
But Clarets keeper Brian Jensen made a fine save from Michael Carrick.
United improved in the second period but Jensen proved the hero as Burnley clung on for a famous victory.
Tottenham are top of the Premier League following a stunning 5-1 win away to Hull, a Jermaine Defoe hat-trick setting Spurs on their way.
Wilson Palacios and Robbie Keane completed the scorers whilst Stephen Hunt grabbed the Tigers consolation.
It was a good night for the promoted teams as Birmingham converted their penalty in injury time to see off Portsmouth 1-0.
James McFadden scored from 12 yards after Pompey keeper David James had clattered Sebastian Larsson.
Liverpool shrugged of defeat in their opening fixture by comfortably disposing of Stoke 4-0 at Anfield.
Two late goals from Dirk Kuyt and substitute David Ngog in injury time added lustre to the scoreline.