Nerves crept around Stade Marcel Michelin as the home team's lead dwindled until Waldrom, on the field for just three minutes as a replacement, was binned for illegally trying to prevent a Clermont drive rumbling any further.
That allowed Wesley Fofana to launch a daring counter attack, eventually halted by Vereniki Goneva.
Clermont dominated the first half, though it was through the boot of Morgan Parra that they led 19 7 at the break.
mazy run as Tigers burst out of defence with Anthony Allen and Tait. Tuilagi looked to have broken clear but was hauled into touch by Naipolioni Nalaga.
Scully out jumped two defenders as Williams almost worked a second score with another kick across field but the scoring pass eluded them.
Leicester paid the price for twice failing to stop Aurelien Rougerie as he drifted across to combine with his midfield partner. Fofana's quick hands released Davit Zirakashvili before racing onto the prop's well timed return pass to score in the 22nd minute.
Leicester fed off scraps but had an early glimpse when Jamie Gibson's turnover allowed Manu Tuilagi to break, only for Mathew Tait to knock on.
Leicester got to within three points entering the final quarter, but last season's beaten finalists held their nerve to advance to the last four where they will face Saracens at Twickenham.
Goneva stepped through tackles on a Omega Seamaster Professional Replica
Fofana threatened with his footwork whenever he touched the ball and was again involved for the opening points on 13 minutes. Thomas Domingo bashed through Louis Deacon and Fofana followed to earn a penalty.
Clermont Auvergne v Leicester
It is five years and now 75 matches since Clermont last lost on their Omega Seamaster Trilogy For Sale
Clermont went close to scoring a second try when Noa Nakaitaci and Jean Marcellin Buttin combined but Tigers managed to get enough bodies under Zirakashvili to prevent the prop grounding the ball over the line.
Parra kicked his fifth penalty put they were the only points Leicester conceded during the 10 minute spell to set up a Omega Speedmaster Mkii tense finale.
They were far more competitive at the breakdown and, at last, their backs had possession to play with.
Tigers mounted a last desperate attack in the final moments and captain Slater came within two metres of the line but Graham Kitchener's over eagerness got the better of him and James was able to clear the danger.
However, Richard Cockerill's side fell just short in the end, after storming back to 19 16 down, as Thomas Waldrom's untimely yellow card midway through the second period proved costly.
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ChanceParra struck a third penalty on the stroke of half time but the try, which was converted by Williams, had shifted the balance in power and Leicester sensed a chance.
two defenders to hand Crane an easy finish close to the posts.
Parra converted from wide and added two more penalties, either side of Williams' striking the post, to steer Clermont further ahead in front of a raucous crowd.
Tigers trailed 16 0 after 35 minutes but Jordan Crane's try and the boot of Owen Williams saw former Heineken Cup winners Leicester come agonisingly close to ending the longest unbeaten home record in Europe.
home patch but they were given a fright by the Tigers. T
Williams found Gibson in acres of space with a pin point cross field kick and Blaine Scully drew the last Omega Speedmaster Olympic
The Welshman did, however, kick three penalties while Parra and Brock James both fired wide to slash the deficit to just three points, at 19 16, on the hour.
The visitors looked to be staring defeat in the face but Crane offered a lifeline before half time.
Leicester also repelled a strong surge by number eight Fritz Lee off the resulting scrum and Julian Salvi seemed to have pulled off a crucial steal, only to be penalised for holding onto the ball and Parra extended Clermont's lead to 16 0.
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