Leeds are now just two points off the play-offs with a game in hand, while Walsall, who have taken only one point from their last four games, have dropped back to ninth.
And there was more good news for Leeds with the appearance of midfielder Jonathan Douglas for the last ten minutes after three months out with a knee injury.
Despite Walsall having five in midfield, it was Leeds who ran the game and almost took an early lead when Dougie Freedman put Beckford clear, but his first-time shot flew just wide.
However the Leeds striker, who had scored only once in Leeds' last 11 games, broke the deadlock in the 29th minute when he took Neil Kilkenny's pass in his stride, rounded the keeper and rolled it into the net.
Walsall were struggling to get into a shooting position against a much improved Leeds. The one time they threatened in the first half, Edrissa Sonko strayed offside.
Instead it was Leeds who looked more likely to extend their lead, David Prutton warming Clayton Ince's hands with a long-range drive.
The Saddlers looked livelier after the break and had a good chance with a free-kick just outside the box, but Lee Holmes clipped the ball over the bar.
And minutes later Tommy Mooney had the goal at his mercy but lashed his shot over.
At the other end, Alan Sheehan drove in a 30-yard free-kick that brought a good save from Ince and the Walsall keeper was on his toes again soon after, when he cleared Bradley Johnson's header off the line.
The home side got their reward ten minutes from time when Beckford's pace took him past the defence and he latched on to another fine pass from Kilkenny and steered his 19th of the season past Ince.