Leeds conceded five at home for just the second time in their history in losing to the Seasiders on Wednesday and would have probably taken a morale-boosting 0-0 draw here were it to have been offered to them before kick-off.
But when they became the first of the sides to take a tepid game by the scruff of its neck with Clayton's 25-yard curler with 69 minutes gone, a maximum-point haul was a reality and their notoriously fragile defence held out to secure a first win over Leicester in nine attempts.
They were rarely tested by Leicester, though, who did not force debutant goalkeeper Alex McCarthy into a meaningful save all afternoon.
A consequence of that was a second loss in three games for caretaker managers Jon Rudkin and Mike Stowell and, although the club were today remaining tight-lipped over an approach for Hull's Nigel Pearson, a permanent successor to Sven-Goran Eriksson will surely be in place by the time City face Crystal Palace in a fortnight's time.
Paul Rachubka, whose three calamitous moments underpinned Leeds' midweek nightmare, was dropped in one of just two changes made by manager Simon Grayson, while Rudkin and Stowell stuck with the side that beat Burnley on Tuesday.
McCarthy, who joined from Reading on Friday, could not have wished for an easier debut in truth, and that was the case from the first whistle, with his only real involvement early on being witness to a Steve Howard half-volley looping over his bar.
At the other end, Leeds' strike pair of Andy Keogh and Ross McCormack both succeeded in turning and getting in behind the Leicester defence, but hesitated and were quickly shut down when a run at goal would have been the better option.
McCarthy then turned a cute Andy King cross-shot over his bar, before McCormack wasted the first genuine opening of the game when he drilled over from 12 yards after an Aidy White cross fell to him with 18 minutes gone.
The Scot's failure to score what would have been an 11th of the season did not signal the start of an open period, though, and the game remained tight and was played largely in the midfield. When opportunities did come, Leicester's Paul Gallagher and Leeds' Danny Pugh dragged them wide.
White was nearly caught out in the first-half injury time when he was robbed by Neil Danns on halfway but, much like Keogh and McCormack before him, Danns could not make the best of the space ahead of him and was crowed out by Jonny Howson.
The pedestrian nature of the game continued into the second half, and a half-hearted scoop from Danns that landed on the top of McCarthy's net was the closest either side went in the opening 15 minutes.
It was going to take something special to break the deadlock and Clayton's strike was just that. Leeds worked the ball wide to Pugh and, after his scuffed cross was cleared, Clayton curled the loose ball beyond Kasper Schmeichel from 25 yards, giving the former United stopper no chance as he found the top right-hand corner.
Leicester immediately sent on £3million striker Jermaine Beckford, who scored 85 goals in 132 starts during a four-year spell at Leeds, but even his arrival could not help fashion a chance for the home side who left the field to a chorus of boos.