It was Leeds' sixth home win in a row, the first time they have done that since a run that started on Boxing Day 2005.
Leeds always looked comfortable, but it took 25 minutes before they found a breakthrough when Ben Parker intercepted a pass and the ball broke to Beckford who drove past Josh Wagenaar.
Beckford had the ball in the net again two minutes later but it was ruled out for offside, but it was all Leeds and it was just a question of time before they scored again.
With three minutes to go to the interval, Neil Kilkenny broke forward and as the Yeovil defence backed off he unleashed a long-range shot that flew into the top corner of the net giving Wagenaar no chance.
Terry Skiverton rung the changes at the start of the second half, sending on Aaron Brown for Danny Schofield and was then forced almost immediately into a second change when Gavin Tomlin went off injured to be replaced by Paul Warne.
But there was nothing Yeovil could do to stop Leeds and Kilkenny opened them up with a sweet pass that gave Beckford his second goal.
Brown's match lasted less than ten minutes and he went off to be replaced by Kieran Murtagh.
And with only 12 minutes of the second half gone, Beckford struck again firing home from just outside the area.
Leeds should have gone further ahead when they were given a penalty. Luciano Becchio refused to give the ball to Robert Snodgrass and then made things worse by firing over the bar. Becchio was immediately replaced by Mike Grella.
The Glovers continued to disappoint, not managing a single shot on target and Leeds were happy to cruise to probably their easiest win of the season.