Beckford wasted three other chances but his 32nd-minute goal was pure class.
The move covered almost the length of the Elland Road field as wingers Andy Robinson and Robert Snodgrass combined to ferry the ball to Beckford, who cut into the penalty box on the right and curled a sublime left-footed shot into the far top corner.
Millwall claimed Gary Alexander's header - 10 minutes earlier - had crossed the line but a TV action replay showed Danish keeper Casper Ankergren make the save on the line before Richard Naylor completed the clearance.
Ankergren was just as alert in sprinting off his line and diving bravely at Izale McLeod's feet to deny the Lions an equaliser five minutes after the break and Leeds had another let-off when Alexander's free-kick flew inches too high from 20 yards.
However, Beckford pounced again in injury time for his 23rd goal of the season, shooting past David Forde when Ankergren's long kick was helped on by substitute Luciano Becchio.