Beckford, who took his season's tally to 17, had been booed against Southampton last weekend for his reaction to being substituted but responded in the best possible fashion in the League One clash on Boxing Day.
Hartlepool took a 25th-minute advantage when Leeds failed to deal with Ritchie Humphreys' corner and Iceland international Armann Bjornsson fired a hard cross-shot into the net.
Leeds' equaliser arrived 13 minutes later. A Robert Snodgrass free-kick was only cleared as far as Neil Kilkenny on the edge of the box and the Australian's low drive was flicked into the bottom corner by Beckford.
The hosts then took the lead in stoppage-time at the end of the first period. Jonny Howson's cross was headed towards goal by Luciano Becchio and the ball deflected in off defender Gary Liddle's back.
Beckford struck the bar in the 53rd minute but grabbed his second goal - and his seventh in five matches against Hartlepool - with 21 minutes remaining after Becchio's flick-on.