Leeds had recalled Snodgrass in place of Bradley Johnson and it was the Scot whose long pass should have set up a goal for Beckford as early as the ninth minute. Beckford looked suspiciously offside but took much too long getting the ball under control and the chance went begging.
Robinson had warned his Leeds team-mates that they would have to toughen up after being out-muscled at the New Den in October and defender Rui Marques went into Alan Wiley's book for a badly-timed tackle which hurt Izale McLeod and incensed Millwall's players.
The Lions complained again in the 23rd minute when Gary Alexander claimed his header had crossed the line after Adam Bolder's free-kick was played to him at the far post by David Martin but keeper Casper Ankergren made an excellent save on the line and Leeds captain Richard Naylor completed the clearance.
After opening the scoring Beckford wasted another opportunity by shooting high and wide and there was another let-off for Millwall when Robinson's hard shot hit a defender and looped inches over the bar.
Millwall stepped up a gear after the break and, after Ankergren had rescued Leeds by swooping on the ball as McLeod was about to shoot, Alexander's 20-yard free-kick was only just too high.
The Lions sent on goal specialist Neil Harris in place of McLeod with 20 minutes left in the hope of pulling the game out of the fire. But it was Martin who went closest, forcing Ankergren into another fine save before shooting just wide from distance.
Beckford then struck again in stoppage time with a low shot after being put through by substitute Luciano Becchio.