United keeper Casper Ankergren made two fine saves in the first half hour from recalled Yeovil striker Jon Obika.
Yeovil, unbeaten in their previous six matches, then had a 36th minute penalty claim rejected when Obika went down under the weight of an Andrew Hughes challenge before the home side seized a 42nd minute advantage through a fortuitous Bradley Johnson goal.
The winger crossed the ball towards the near post where Beckford narrowly failed to get a touch, but Glovers goalkeeper Alex McCarthy allowed the ball to zip through and into the far corner for Johnson's seventh goal of the season.
Substitute Max Gradel underlined Leeds' second half improvement by taking a pass from Leigh Bromby on the right and scoring from a narrow angle with 20 minutes remaining
Beckford was twice denied by an offside flag but his patience was rewarded when he pounced on a mistake by Terrell Forbes and shot into the top corner in the 79th minute. Two minutes later Robert Snodgrass' cross allowed substitute Tresor Kandol to head in Leeds' fourth.