Beckford had done everything but score before popping up with his sixth goal in his last four matches with four minutes remaining.
It had looked like a rare Tom McMahon goal would give Middlesbrough victory when he struck in the 79th minute.
Scott McDonald had earlier cancelled out David Nugent's opener for Leicester to send the teams into half-time level.
The draw still saw Boro climb back into the npower Championship play-off places.
In-form striker Beckford recovered from a tight hamstring to enable Leicester manager Nigel Pearson to name an unchanged starting line-up.
New signing Wes Morgan was on the bench following his arrival from east midlands rivals Nottingham Forest.
Middlesbrough were forced into one change with Jason Steele replacing the injured Danny Coyne in goal.
The visitors were the first to threaten after five minutes with Barry Robson sending a shot narrowly wide from just outside the area.
Two minutes later, Leicester took the lead. The ball was hooked into the box from the right and Nugent headed home at the far post from three yards out.
Boro were almost level in the 14th minute when Foxes captain Matt Mills sliced a clearance that had Kasper Schmeichel scrambling across his goal. Fortunately for the hosts the ball bounced wide.
Soon afterwards Marvin Emnes hit a half-volley from the edge of the area that had to be pushed away by the Leicester goalkeeper diving to his right.
Boro equalised after 16 minutes. McMahon's corner was flicked on at the front post by Seb Hines and McDonald applied the finish from a yard out.
Leicester produced the move of the match just before half-time.
Beckford collected the ball out on the right and cut inside before playing it into Nugent on the edge of the box and continuing his run.
Nugent laid a first-time pass off to Lloyd Dyer, who dinked the ball over the top for Beckford but his shot just cleared the crossbar.
Steele then had to produce a fingertip save in first half stoppage time to thwart the former Leeds and Everton striker once more.
Beckford threatened again on the hour when a mazy run into the box had to be halted by Steele smothering the ball at his feet.
Pearson made two changes immediately afterwards, handing home debuts to Danny Drinkwater and Nathan Delfouneso. Paul Gallacher and Dyer were the men to make way.
Middlesbrough manager Tony Mowbray responded with a double substitution of his own in the 69th minute. Kevin Thomson, available again after suspension, and Malaury Martin replaced Robson and Emnes.
Beckford seemed the man most likely to come up with a winner and he almost conjured something magical again midway through the second half but his hooked, left-foot volley from the left side of the area struck the crossbar.
McMahon may have thought he had sealed Boro's first league win since Boxing Day with a superbly-taken free-kick 11 minutes from time.
It was the first time the 25-year-old had bothered the scoresheet since netting in a 3-2 win at Millwall on February 19, 2011.
But Beckford had other ideas and the lively striker got the goal he deserved in the 86th minute.
McMahon's back pass always lacked pace and Steele was forced out of his goal to try to clear.
But his kick struck the onrushing Beckford and bounced goalwards, enabling the Leicester striker to level things up with a simple tap-in.