Beckfordscored in the 19th minute when he beat the Manchester United's backline to a 50-yard ball from Johnny Howson and beat goalkeeper Tomas Kuszczak.
Beckford could be sold to Newcastle during the January transfer window for as much as $4 million.
"There will be three scenarios with Jermaine," said Leeds manager Simon Grayson. "Either he signs a new contract, leaves at the end of the season for free or we sell him and get money which we think is too good to turn down. Jermaine showed what he's all about with his goal. He worked ever so hard for the team, took his opportunity and now has five goals in his last three games."
Leeds was once one of the dominant teams of English soccer and had a great rivalry with Manchester United, but it ran into financial problems and went into bankruptcy. But Grayson has the club in first place in League One as its turnaround continues.
Ferguson ripped into his players after the game.
"I didn't expect that," he said. "I was shocked at the performance. Human beings can always surprise you, but we didn't expect that today. I don't think any of the players can say they had a good day. OnlyAntonio Valencia, when we got the ball to him, but it took us 10 minutes to do that. We never got going and the quality of passing -- the whole performance was bad."
Ferguson also ripped into the refereeing -- again -- calling Chris Foy's decision to add only five minutes of stoppage time an "insult."
The 67-year-old Scotsman served a two-match ban this season for criticizing referee Alan Wiley and was warned about facing further suspensions if his attacks continued.
American Mike Grella was on the bench for Leeds.
Jan. 4 in Manchester
Man. United 0 Leeds 1.Goal: Beckford 19
Manchester United --Kuszczak, Neville, Brown, Evans, Fabio Da Silva, Obertan (Giggs, 57), Gibson, Anderson (Owen 69), Welbeck (Valencia, 57), Berbatov, Rooney.
Leeds --Ankergren, Crowe, Naylor, Kisnorbo, Hughes (White, 90), Howson (Snodgrass, 79), Kilkenny, Doyle, Johnson, Becchio (Michalik, 89), Beckford.