Tottenham Hotspur 2 Leeds United 2
Leeds, who were conquerors of Manchester United in the previous round, had looked set to exit the competition at the hands of more Premier League opposition.
But coveted striker Beckford - the League One club's hero at Old Trafford - held his nerve to power home a spot-kick in the fifth minute of stoppage time to keep Leeds in the competition.
Spurs had twice led and took the lead for the first time on the stroke of half-time through Peter Crouch.
Jermain Defoe and then Niko Kranjcar has tasted visiting keeper Casper Ankergren in the early stages of a pulsating encounter.
Ankergren looked in inspired form and dived to his right to turn away Defoe's spot-kick after the lively England striker had been felled in the box by Michael Doyle.
However, the Danish keeper could do little when Crouch was on hand in the 42nd minute to tuck away the rebound after Kranjcar's shot had been spilled.
Leeds were back on level terms just seven minutes into the second half when Beckford scrambled home a scruffy equaliser after Spurs had failed to clear a corner.
Spurs boss Harry Redknapp looked worried and sent on Wilson Palacios, Roman Pavlyuchenko and Robbie Keane.
His changes appeared to have the desired effect when the much-maligned Pavlyuchenko was the architect of a second goal for the home side.
The Russia striker dummied the ball and then collected Defoe's return before planting a confident shot past Ankergren in the 75th minute.
Spurs then looked in control of the match and were just seconds away from ensuring they were in the hat for the next round when Michael Dawson brought down Beckford.
The striker dusted himself off and confidently dispatched the spot-kick past Heurelho Gomes to set up a replay at Elland Road.