Beckford, who Scunthorpe wanted to buy following an impressive loan spell at Glanford Park last year, made no mistake from close range in the 80th minute after David Prutton's shot had hit the crossbar.
Scunthorpe had stolen the lead early in the second half when summer signing Gary Hooper coolly converted into the bottom from 12 yards but Leeds hit back almost immediately through new striker Enoch Showunmi and went on to run out deserving winners.
Leeds were denied by a controversial decision on the stroke of half-time when a shot-cum-cross from Robert Snodgrass appeared to have been dropped by Scunthorpe goalkeeper Josh Lillis over his goalline.
Scunthorpe struck in timely fashion in the 57th minute as Leeds appeared to have seized control. Paul Hayes and Hooper combined inside the box to leave Rui Marques on his backside and the latter finished confidently into the bottom corner.
But Leeds were back on terms within four minutes when Showunmi outjumped the home defence to head Snodgrass' cross into the top corner. Lillis pulled off another impressive save to deny Beckford but was helpless when the Leeds striker fired home a rebound when another Prutton thunderbolt came back off the woodwork.