Leeds fans reacted by booing their 15-goal striker's petulance and chanting Grayson's name. Two minutes later Robert Snodgrass scored the only goal of the game.
Receiving a pass on the left from Andrew Hughes the Scot curled a right-foot shot into the far top corner.
Luciano Becchio wasted the best chance of a keenly contested first half when, unmarked at the near post, the Argentine headed over from a perfect cross by Snodgrass in the 38th minute.
Beckford squandered several opportunities, his close control repeatedly letting him down and leaving him frustrated.