Leicester City 0 Leeds United 1
Clayton's 25 yard curling strike came with just over twenty minutes remaining and was a highlight in an otherwise lacklustre encounter between two promotion hopefuls in which the home side were condemned to their fourth home loss of the campaign.
Leicester played well in parts but struggled to create any clear cut chances after being frustrated throughout by a resolute Leeds defence.
Caretaker managers Mike Stowell and Jon Rudkin made no changes to the Leicester side that beat Burnley 3-1 at Turf Moor during the week, and the Foxes started brightly with some good build-up play between Paul Gallagher and David Nugent, before Steve Howard volleyed over the bar from eighteen yards.
Robert Snodgrass then tested his former team-mate and Leicester goalkeeper Kasper Schmeichel at the near post after Andy Keogh had won a corner for the visitors following Sol Bamba's important block.
Richie Wellens had a dipping shot tipped over the bar by Andy Lonergan after fifteen minutes, while Ross McCormack fired high and wide at the other end of the pitch.
Paul Gallagher should have tested Lonergan just after the half-hour mark but dragged his shot well wide of the far post to sum up a fairly uninspiring first period.
Leicester showed more energy after the interval and came close to breaking the deadlock when his shot was deflected over the crossbar after excellent work from Richie Wellens.
David Nugent then had a shot blocked before Leicester had a penalty appeal turned down on the hour mark after Wellens appeared to have been brought down inside the penalty area.
But it was the visitors who went ahead with twenty minutes remaining when Adam Clayton took advantage of the Foxes' failure to close down a Leeds counter attack by curling the ball past the outstretched Kasper Schmeichel from 25 yards.
The goal was a strike worthy of winning any game, and the only real difference between the two sides on the day.
The goal spurred Leicester into making a double substitution; former Leeds man Jermaine Beckford replaced Steve Howard, while Neil Danns made way for Michael Johnson.
Beckford immediately looked sharp and was unfortunate not to latch onto the end of Kasper Schmeichel's long goal kick, before the Danish shot-stopper made a fine near-post save to keep out a strike from Robert Snodgrass.
Former Leicester defender Patrick Kisnorbo then made a vital stop to keep out Jermaine Beckford's goal-bound effort with ten minutes to go as Leicester continued in search of an equaliser.
But Paul Konchesky's wild strike from distance flew well wide of the goal with tow minutes remaining was Leicester's last real chance to draw level, and the final whistle indicated a second successive home defeat for the managerless Foxes.