It seemed Colin Calderwood's side were the more likely to claim three points as substitute Felix Bastians lashed narrowly wide in the 88th minute.
Forest had fought back strongly after going behind to Tresor Kandol's 17th minute opener, with Kris Commons levelling when his cross from a free-kick curled straight into the back of the net.
And it was the Reds who had been on top in the final stages until Beckford pounced to help Dennis Wise's team claim their third straight win in League One and leave Forest looking for their first.
Calderwood will have been encouraged by the start his side made to the match as 15 minutes of domination saw Forest come close to snatching a deserved lead.
But, while James Perch saw his low shot charged down with what was the home side's best chance of their spell in the ascendancy, Leeds were far more ruthless.
The quick break lead by Beckford was their first genuine attack of the match, but once he had fed his strike partner, Kandol, the forward made no mistake with a low finish from 12 yards that bounced into the net off the inside of the post.
After that it was Leeds who grew in confidence, with Kandol and Beckford both guilty of mis-firing when presented with decent chances to double their advantage.
While Forest had keeper Paul Smith to thank as he made a superb save to deny David Prutton - who finished last season on loan at the City Ground - from making a scoring return as he palmed the midfielder's firm header over the bar.
The home side's only other real chance of the first half came through a Sammy Clingan free-kick that looked to be arrowing goalwards until taking a deflection.
The mood changed after the interval as Forest began an immediate quest for an equaliser, which they earned after only four minutes of pressure.
Alan Thompson was booked for a foul on Clingan on the far side, but the punishment for the Leeds skipper was more severe as, from the resulting free-kick, Commons fired in a pacy cross that, with the aid of a deflection from Thompson, found its way into the back of the net.
Perch slid a low shot inches wide of the post as Forest went in search of an immediate second, while Commons also bent another effort narrowly the wrong side of the upright.
Substitute Bastians came agonising close to putting Forest ahead as the home side piled on the pressure.
But it was to be Leeds who triumphed as Beckford kept his head to fire high into the roof of the net.