The striker scored a hat-trick in the FA Cup demolition of Northampton on Monday and took just 15 minutes to open the scoring in this League One clash when he expertly glanced home a right-wing cross from Andrew Hughes.
However, the lead lasted just 11 minutes before Hartlepool exposed Leeds' defensive problems. Michael Nelson lifted the ball into the goalmouth from just outside the penalty area after a partially cleared corner and Joel Porter was unchallenged as he headed his 11th goal of the season.
Hartlepool goalkeeper Arran Lee-Barrett made excellent saves to deny Beckford and Luciano Becchio but the visitors were dangerous down the flanks and efforts by Porter and James Brown went close.
Leeds were back in front five minutes after the break when Jonathan Douglas and Becchio released Fabian Delph who shot low into the net from 12 yards.
Kevin Kyle shot against the Leeds crossbar but Hartlepool fell further behind in the 64th minute when Beckford nudged a long clearance from keeper David Lucas to Becchio who blasted the ball home from eight yards. Then Beckford took a pass from Hughes to hit Leeds' fourth in stoppage time.