Leinster (20) 29
Tries: Heaslip 2 Cons: Sexton 2 Pens: Sexton 5
Clermont Auvergne (10) 28
Tries: Malzieu 3 Cons: James 2 Pens: James 3
Rob Kearney is tackled by Alex Lapandry and Aurelien Rougerie
Heineken Cup holders Leinster beat Clermont Auvergne by the narrowest of margins to progress to the semi-finals of this year's competition in Dublin.
A Julien Malzieu try helped the French side to a 10-0 lead but two fine Jamie Heaslip tries saw Leinster recover to lead 20-10 at the interval.
Malzieu scored two further tries as his side moved five points ahead but then Jonathan Sexton kicked two penalties.
Brock James had a late drop-goal to win it for Clermont, but pushed it wide.
James completely miscued an early penalty attempt but Malzieu put Clermont ahead by scoring in the corner after James set up a swift move with a delicate chip in the 12th minute.
The French side's fly-half added the conversion to make it 7-0 and then kicked a penalty to extend his side's advantage.
Sexton was successful with a straightfoward penalty in front of the posts and a converted try then drew Leinster level.
Brian O'Driscoll created space with a trademark jink and passed to Heaslip who showed power and pace to surge through attempted French tackles and score in the corner.
Sexton converted and James missed with two kickable penalties as Clermont squandered their chances to move ahead.
Heaslip scored his second try of the game under the posts on 34 minutes and Sexton's conversion and another penalty three minutes later gave the home side a 10-point lead.
Morgan Parra missed with his penalty effort late in the half, having temporarily assumed place kicking responsibilities from the off-colour James.
The Leinster forwards set up the platform for Malzieu's second try four minutes after the break, but James was unable to convert.
James knocked over a penalty to reduce his side's deficit to two points but a Sexton penalty gave the holders some breathing space.
James knocked over his third penalty of the game and Malzieu completed his hat-trick of tries in the 61st minute.
Shane Horgan's attempted clearance kick was charged down and the ball fell to Malzieu, who went on a mazy run before touching down. James kicked the conversion.
Leinster immediately went on the attack but the referee ruled that Eoin Reddan had not managed to cross the Clermont line after consulting the television official.
Sexton kicked another penalty but missed with another attempt after Clermont full-back Anthony Floch had been yellow-carded for a deliberate knock-on.
Sexton missed the resultant penalty but was successful with his next attempt to nudge Leinster one point ahead.
The French side had two late opportunities to steal victory but James was wide with both drop-goal attempts when well placed.
Leinster, who had Rob Kearney stretchered off late on, await the winners of the all-French tie between Toulouse and Stade Francais in the semi-finals.
Leinster: R Kearney, S Horgan, B O'Driscoll, G D'Arcy, I Nacewa, J Sexton, E Reddan, S Wright, J Fogarty, C Van Der Linde, L Cullen [capt], N Hines, K McLaughlin, S Jennings, J Heaslip.
Replacements: B Jackman for Fogarty (74) , M Ross, C Healy for van der Linde (41), M O'Kelly, S Keogh, P O'Donohoe, S Berne, G Dempsey
ASM Clermont Auvergne: A Floch, A Rougerie [capt], M Joubert, G Canale, J Malzieu, B James, M Parra, T Domingo, M Ledesma, D Zirakashvili, J Cudmore, T Privat, J Bonnaire, A Lapandry, E Vermeulen.
Replacements: B Cabello for Ladesma (74) , V Debaty for Domingo (71), C Ric, J Pierre for Privat (53), A Audebert for Lapandry (53), K Senio, G Williams, W Fofana
Referee: David Pearson (England)