Garry Ringrose made up for missing the last two big Aviva Stadium occasions with two tries and an assist - as Leinster hit the Tigers for seven on their way into the last four for the 14th time.
Ringrose missed last Saturday's last 16 victory over Ulster on Lansdowne Road as a result of the concussion suffered on duty for Ireland at Murrayfield last month.
The head injury also forced him to sit out Ireland's Grand Slam clincher against England at the same ground.
Restored to the starting line-up last night, he waltzed in behind Leicester's bemused defence twice in the opening 17 minutes to put the province on their way.
Then, with Caelan Doris' binning reducing Leinster to 14 men in the third quarter, Ringrose broke clear again to set up Jamison Gibson Park for the killer third.
Leicester's stubborn resistance was broken - and the floodgates opened.
With Toulon or Sharks providing the semi-final opposition - also at the Aviva - in three week's time, Ryan Baird (shoulder) and James Lowe (thigh) could face a race to be fit, although Josh van der Flier will be back.
Cullen's men were big favourites to keep their season-long unbeaten run going. Leicester were limited but made life difficult at the breakdown and with their all-round physical approach - for 55 minutes, at least.
Ringrose only needed 75 seconds to announce his return. Hugo Keenan was first to Ross Byrne's kick-off and Leinster took it from there, with Ringrose's feint fooling Tigers centre Dan Kelly and he was in under the posts, making it an easy conversion for Byrne.
Tadhg Furlong had to come off to get stitched up and, in his absence, Leicester found a quick response through Handre Pollard's seventh minute penalty - conceded by Leinster's front row at scrum time.
With Furlong restored, Leinster won a scrum penalty of their own - and weren't in trouble again in that regard.
In the 17th minute, the Blues were celebrating behind the Tigers' posts again when, off scrum ball, Byrne and Jimmy O'Brien combined to release Ringrose in space as the visitors were torn apart.
Byrne converted and then extended the lead with a 31st minute penalty - but it was Leicester who scored next just before half-time to keep the contest alive.
Dan Sheehan, first, then Lowe were penalised - and Mike Brown charged up close to Leinster's line and Anthony Watson crossed in the corner for a 17-10.
With Pollard's touchline conversion, it felt like game on - even more so when Doris was shown a 46th minute yellow card for a high challenge on Jasper Wiese.
Instead, Leinster scored 10 points while he was off the pitch. Byrne fired over another penalty earned at the scrum before Ringrose's perfectly timed run saw him glide into space again. He had options on either side and passed inside to Gibson-Park to score.
A penalty try off a lineout maul quickly followed and Leinster were now rampant, with Baird's replacement Scott Penny adding to his prolific try record in the 61st minute and Byrne nailing the tough extras.
The Tigers mustered a converted try in response through Pollard only for O'Brien to gallop in at the other end. Byrne maintained his 100% record with the conversion.
With five minutes remaining, Tigers centre Harry Potter ran from deep to score but John McKee had the last say with Leinster's seventh to push the Blues beyond the half century mark.
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