Leicester City 3 Birmingham City 1
The visitors took an early lead when Wade Elliott converted from the penalty spot, but Beckford drew the Foxes level with a close range finish.
Substitute Jeffrey Schlupp put the hosts ahead with just over ten minutes remaining, before Beckford raced ahead of the Birmingham defence to score his second and Leicester's third in second-half stoppage time.
It was a must win game for Nigel Pearson's side who, despite an inconsistent season, are still just six points outside the Championship playoff places, ahead of an FA Cup quarter-final trip to Chelsea on Sunday.
After a slow opening, Neil Danns' low drive on goal was the first real chance for either side, but Birmingham goalkeeper Boaz Myhill was equal to it, pushing the ball past the post.
David Nugent headed wide moments later before Wade Elliott's tame shot on goal at the other end did little to test Kasper Schmeichel.
Birmingham were then awarded a penalty against the run of play when Sol Bamba was adjudged to have obstructed Nikola Zigic inside the area, with Wade Elliott making no mistake from twelve yards in putting Chris Hughton's side 1-0 up.
It was a harsh decision by referee Mick Russell to award the spot kick, with both Bamba and Zigic appearing to tangle inside the box.
Leicester continued to play the better football as Paul Gallagher, making his return to the starting XI, did well to fire the ball across goal, but there was nobody in a blue shirt on hand to trouble Boaz Myhill.
Zigic then saw his powerful header strike the underside of the bar, as Leicester scrambled the ball away in what might have been game over for the Foxes.
Leicester found an equaliser after 34 minutes when David Nugent beat the Birmingham defence to a loose ball before firing across goal, and although his shot hit the foot of the post, his strike partner Jermaine Beckford made no mistake from close range, firing his side level.
The goal had been coming for the home side and Leicester were good value for their equaliser after Beckford and Nugent had threatened for the opening 35 minutes.
Lloyd Dyer's powerful near post strike was parried away by Boaz Myhill in first-half stoppage time as Leicester looked to take the lead before the break, while Andros Townsend had a glorious opportunity to restore Birmingham's advantage but fired over at the back post.
Leicester continued where they left off in the second-half and could have gone ahead ten minutes after the break when Paul Gallagher whipped a free-kick into a dangerous area, but a mix-up between Sean St. Ledger and Sol Bamba resulted in the ball falling harmlessly to Myhill.
Chris Burke's speculative 25-yard strike was then parried wide by Kasper Schmeichel, before Wellens tested Myhill with a long range strike of his own - the rebound falling to Jermaine Beckford who should have done better from close range, but his overhead kick sailed over the crossbar when the former Leeds and Everton striker probably had more time.
Neil Danns' shot was deflected wide after a quick counter attack through Lloyd Dyer, before Jermaine Beckford hit the outside of the post from close range - although he was adjudged to have used his arm to control the ball in the process.
Dyer then hit the side netting after a mazy run into the box, before Tom Kennedy's route one ball picked out substitute Jeffrey Schlupp who raced behind the Birmingham defence, the Ghanaian making no mistake in coolly slotting the ball past the oncoming Boaz Myhill from eighteen yards, who appeared to have been caught in two minds.
It was a deserved goal for Leicester who had maintained a level of energy and consistency throughout the match which will have pleased manager Nigel Pearson.
Birmingham went in search of an equaliser with ten minutes remaining and came close when Wade Elliott's fine strike from 25 yards flew inches over the crossbar, but Leicester could have doubled their advantage when Jermaine Beckford played a low ball across goal, but it was just too heavy for Lloyd Dyer.
With the last kick of the game, Leicester did get their third when Jermaine Beckford latched on to Sean St. Ledger's long ball and found himself one-on-one with Myhill, and, like Schlupp had done earlier, made no mistake in finding the back of the net to secure an important win for the Foxes.
It was a vital win for Leicester City to keep their playoff hopes alive after successive league defeats, but Nigel Pearson's men will now draw their attention to their FA Cup quarter-final trip to Stamford Bridge this Sunday against Premier League Chelsea.