Robbie Blake, 33, scored in the 19th minute with a spectacular shot and Burnley held on to beat United.
Just before halftime, United was awarded a penalty kick, but Burnley keeper Brian Jensen made a diving save on Michael Carrick's shot.
"You wonder whether it's fate," United manager Alex Ferguson said. "Burnley back in the Premier League -- it's been a long time. They worked hard, they worked their socks off and the fans were fantastic."
Wayne Rooney's inaccuracy in front of the Burnley goal prompted its fans to chant, "You're not Robbie Blake!" New signing Michael Owen came off after an hour, having had no impact on the game.
"We're disappointed and it wasn't a great performance by us," Ferguson added. "It was Burnley's night -- so many things happened in their box I don't know how we didn't score. With the chances we had, we should have won."
Birmingham 1 (McFadden 90-pen) Portsmouth 0
Burnley 1 (Blake 19) Man. Utd. 0
Hull 1 (Hunt 25) Tottenham 5 (Defoe 10, 45, 90, Palacios 14, Keane 78)
Liverpool 4 (Torres 4, Johnson 45, Kuyt 78, Ngog 90) Stoke 0
Sunderland 1 (Bent 18) Chelsea 3 (Ballack 52, Lampard 61-pen, Deco 70)
Wigan 0 Wolves 1 (Keogh 6)