Beckford can expect a telling-off from Simon Grayson after angrily shrugging aside the Leeds manager's handshake as he was substituted with 15 minutes left.
Leeds fans reacted by booing their 15-goal striker's petulance and chanting Grayson's name.
Two minutes later 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.
Leeds remain top of League One after condemning Southampton to their first defeat in eight games.