Marino Keith's own goal just before the interval condemned The Pilgrims to their first reversal at Home Park since September last year - their only defeat as they claimed the Second Division title.
The deciding goal came two minutes from the break when a corner was floated into the box and, after a scramble, a shot from United skipper Paul Butler skimmed off the head of Keith into the back of the net.
The goal came seconds after Argyle had failed to clear their lines, despite a goalline clearance from Peter Gilbert to keep out Simon Walton's thundering drive.
Keith had an almost immediate chance to restore parity before half-time but Leeds goalkeeper Neil Sullivan reacted smartly to turn away his shot after Clarke Carlisle's uncharacheristic mistake.
Leeds, unchanged from the side that had beaten Coventry three days previously, had few moments of concern in the second period, with Argyle's best chance falling to Lee Hodges deep into injury-time.
His drive, though, was easily tipped over the crossbar by Sullivan.
Sullivan's Argyle counterpart, Romain Larrieu, recalled for the first time in more than a year, was also in fine form.
He made two world class saves to deny Brain Deane's point-blank shot in the first half, and turn away Leeds substitute Matt Spring's deflected rising drive in the second.
After a dream start to life in the Coca-Cola Championship, which they briefly led, Argyle now have a clear indication of the task ahead of them.