Skipper Ian Roper's 63rd-minute header had put the Poppies on course for a famous FA Cup giantkilling - but Beckford pounced from close range on 77 minutes to earn the runaway League One leaders a replay.
Kettering started brightly and debutant Richie Partridge fired straight at goalkeeper Casper Ankergren from the edge of the box before curling another effort just wide from 15 yards but Leeds soon settled into their stride and the influential Robert Snodgrass saw his header cleared off the line by John Dempster from Beckford's deep cross.
The Poppies then had an almighty double let off when Beckford fired against the bar from 12 yards and Snodgrass blasted the follow up against the post from the edge of the box.
Roper put Kettering ahead against the run of play with a towering header from Partridge's free kick that went in off the underside of the bar. But Beckford netted his 14th goal of the season to equalise for Leeds when he poked in Snodgrass' fierce cross shot 13 minutes from the end.
Michael Doyle and Jonathan Howson both missed good chances to win it for United late on, while Simon Heslop was denied by Ankergren at the other end.