Beckford, who is expected to leave Leeds for Newcastle United this month, scored on 19 minutes to become the first Leeds player since Brian Flynn to score a winner at Old Trafford.
The defeat for United also ensured that Sir Alex Ferguson experienced a third round exit for the first time. It was United’s first defeat to lower league opposition in the FA Cup since a 2-0 defeat at Bournemouth in 1984.
United manager Ferguson had vowed to field a strong team against the Elland Road outfit, but the Scot performed a selection about-turn by naming youngsters Darron Gibson, Gabriel Obertan and Fabio da Silva in his starting line-up.
Having seen a half-strength team defeat Spurs in the Carling Cup quarter-final last month, however, Ferguson would have expected his players to repeat that performance against an opponent from the third tier.
But the Premier League champions were outfought by Leeds from the kick-off and the sheer intensity of the fixture appeared to catch many of United’s players by surprise.
Ferguson had spoken of the bitter rivalry between the two clubs in the build-up to the game and how his players could expect a raucous atmosphere with Leeds backed by 9,000 travelling fans.
The message apparently didn’t sink in, though, and Grayson’s team were the first to every ball in a ferociously fought encounter.
So United could have no complaints when Beckford put Leeds ahead on 19 minutes with what could be his last goal for the club.
Jonny Howson’s stunning 40 yard pass found Beckford 25 yards from goal and the forward escaped Wes Brown before guiding a left foot shot into the far corner past goalkeeper Tomasz Kuszczak.
United attempted to respond, but Leeds matched fire with fire, with captain Richard Naylor joining Brown in referee Chris Foy’s notebook.
Wayne Rooney was denied an equaliser on 25 minutes, though, when full-back Jason Crowe cleared his goalbound effort off the line.
Other than that near miss, however, United struggled to test Leeds goalkeeper Casper Ankergren and it was the visitors that looked likelier to add to the scoring.
The game threatened to boil over 48 minutes when Brown’s late tackle on Michael Doyle prompted both sets of players to confront each other on the edge of the United penalty area.
Once the game settled down, Leeds continued to take the game to United and Beckford should have made it 2-0 on 78 minutes when he sprung the offside trap before shooting wide of the far post.
And substitute Robert Snodgrass rattled the United crossbar with a 20-yard free-kick on 80 minutes.
Despite finishing the game with Rooney, Dimitar Berbatov and Michael Owen on the pitch, though, United just could not find the goal to save the tie and avoid humiliation.