It was all too easy for Leeds against an injury-hit Northampton side which offered little in attack, whilst being guilty of some poor defending.
Beckford's pace caused problems for the Cobblers throughout the game, particularly in the first half and Leeds effectively had the game in the bag by half time.
Beckford shot Leeds into a 13th minute Lead, racing on to David Prutton's flick on to beat Frank Fielding with a clinical first-time finish.
Beckford twice went close to adding a second before Andy Holt missed a great chance to equalise in the 26th minute when he shot wide following a goalmouth scramble.
Leeds increased their lead in the 28th minute when home skipper Mark Hughes could only deflect a Jonathan Howson shot past Fielding after the midfielder exchanged passes with Malcolm Christie.
Ben Parker grabbed a third goal in the 41st minute when Fielding completely misjudged a speculative 35-yard drive and saw the ball end up in the back of his net.
Leeds keeper David Lucas was forced into action in the first half, producing fingertip saves to deny Liam Davis and then to keep out a deflected Danny Jackman free-kick.
Jason Crowe gave Northampton a glimmer of hope in the 44th minute, heading home a Jackman corner, but Beckford quickly restored Leeds' three-goal advantage in first-half stoppage time, cutting in from the left to beat Fielding with a fierce drive.
Beckford completed his treble ten minutes after the restart when he raced on to Neil Kilkenny's defence-splitting pass to round Fielding and put the tie beyond doubt.
Leon Constantine should have scored against his former club in the 69th minute with just Lucas to beat, but he allowed the keeper to save his weak effort.
Crowe grabbed a late consolation for the Cobblers in the 90th minute getting the final touch following a Luke Guttridge corner.