Beckford struck from two yards out, 13 minutes after Ben Strevens had stunned the home crowd by snatching a 59th-minute opening goal for Brentford.
Brentford's best opportunity of the first half fell to the unmarked Sam Wood but Casper Ankergren was quick off his line to make a desperate save. Leeds finished the first half strongly, Beckford and Gary McSheffrey going close to breaking the deadlock.
But Brentford took a shock lead. Kevin O'Connor's corner was helped on by Leon Legge to Charlie MacDonald. His shot was parried by Ankergren but Strevens forced the ball over the line from a few yards out.
Beckford had endured a frustrating afternoon until his 72nd-minute leveller. Robert Snodgrass's cross from the right found McSheffrey beyond the far post and his deflected pass into the goalmouth was side-footed in by Beckford.
Leeds could have won it but substitute Lubo Michalik headed against a post in the 90th minute.