Robbie Blake's smart volley from outside the box in the first half prove gave Burnley a memorable victory after United's Michael Carrick saw his penalty well saved by Brian Jensen just before the break.
Michael Owen, partnering Wayne Rooney in a disappointing United attack, was replaced after the hour by Dimitar Berbatov but their attempts for an equaliser were stopped by an inspired Jensen.
Elsewhere, a Jermain Defoe hat-trick helped Tottenham Hotspur to a 5-1 victory at Hull City to make it two wins from two, while Birmingham City beat Portsmouth 1-0.
Liverpool's match at home to Stoke City started at 1900GMT.
(Reporting by Neil Maidment; Editing by Kevin Fylan)