Six minutes in at the Aviva Stadium, Jack Carty had a very kickable penalty on the Leinster 22 to put Connacht ahead in the second leg of this round of 16 tie.
Carty missed, and it was almost completely one way traffic thereafter as pretty much everything that could go wrong did go wrong for the westerners and Leinster cantered into the quarter-finals in front of a crowd of 32,064.
There the Blues are likely to face Premiership leaders Leicester Tigers, who hold a 29-10 lead over Clermont Auvergne after their first meeting.
Leo Cullen's men will know for sure who they will face in the last eight by around 7pm tomorrow and, while content with what a lot of what he saw this evening, the Blues boss will focus on his side's slow start for the second game in a row.
However the four-time champions were ruthless when they had to be and it was a case of contest over well before half-time.
Fittingly, it was James Lowe who ended the game with the last try with the clock into the red.
It was his fourth try to finish off yet another outstanding outing by the Ireland star and Leinster scored eight converted tries in total.
"It doesn't matter who it is, whether it's Leicester or Clermont we'll focus on us," said Lowe.
When Connacht were reduced to 13 men in the 53rd minute - in a scenario not quite the same as the one Ireland faced against Italy - it meant nothing to the outcome.
Connacht were the big underdogs as they played at the knock-out stage in the competition for the first time but it was they who made a rousing start in Galway last Friday - and it was a very similar story on Lansdowne Road as the visitors made all the early running.
Indeed, their five point deficit after the first game was reduced to two by the third minute of the second, as Carty slotted over the fixture's first penalty when Andrew Porter - back for the first time after his Six Nations injury - held on too long in the ruck under pressure from Connacht flanker Cian Prendergast.
Moments later, Hugo Keenan could count himself fortunate that he wasn't sent to the sin-bin for catching Tiernan O'Halloran in the air under Johnny Sexton's up and under, with only a penalty awarded.
Full of intent, Connacht were instantly on the charge again and a Carty kick-through for Mack Hansen was bundled into touch by full-back Keenan.
As Leinster defended their line, Caolan Blade's attempt to out-fox the Blues as he cut inside and drew a penalty for offside.
Skipper Carty pointed to the points as he looked to deliver the psychological blow of kicking Connacht ahead on aggregate, but he miskicked wide of the far post.
The 30-year-old made some amends with a superb kick deep into Leinster territory but that was as good as it got for Andy Friend's side for the remainder of a torrid opening half from their viewpoint.
Shaking off the early rust, Leinster gradually eased into full stride and struck for the first of four first half tries in the 10th minute.
The westerners were stretched on their left flank by a clever attack. James Lowe, who was their tormentor in chief last week, was involved twice, and Connacht's summer signing Josh Murphy was also instrumental as Jamison Gibson-Park was handed a clear run in for the try.
Sexton's conversion was on the money and, after Porter gained a little revenge with a breakdown penalty win of his own, Robbie Henshaw wrestled free of Ireland colleague Bundee Aki's challenge off Lowe's perfectly-timed pass to power over.
Hansen relieved the pressure momentarily with an audacious pass out of the tackle close to his own line to O'Halloran, who cleared the danger.
It was but a brief respite. Josh van der Flier's ball carrying has been an added bonus for Leinster and Ireland this season and the flanker's powerful surge opened the door for Tadhg Furlong to dive over in the 28th minute, the heft of Ross Molony propelling the tighthead over.
Sexton knocked over both conversions and did the same with the four penalty with four minutes of the half remaining after Lowe backed himself rather than off-loading to Garry Ringrose, and the winger did well to touch down.
It was simply another painful body blow for Connacht, who had lost Aki to the sin-bin seconds before when he caught Sexton without wrapping in the tackle.
So it was 28-3 at the break and Leinster held a 33 point aggregate advantage that was advanced to 40 points just two minutes after the restart.
This was the hosts in full flow as Rhys Ruddock - a 38th minute replacement for Jack Conan, who had earlier suffered an injury but had played on - took off down the left before the ball was worked into the hands of Jimmy O'Brien on the right.
He came close to the Connacht line before Gibson-Park and Sexton moved the ball left to Henshaw, who had acres of space to run into before dotting down.
The visitors then lost Finlay Bealham to a HIA when he clashed heads with a team-mate at the ruck, his legs buckling under him in alarming fashion, but he was able to walk off the pitch after treatment.
And Connacht fans finally had something to cheer about when their side finally scored a try two minutes later.
Aki, who had just returned to the contest, ran a vital decoy run as Carty found O'Halloran, who crossed the whitewash, though Carty was again off-target.
Soon after, Friend's side paid the price for indiscipline. Bealham's replacement Jack Aungier tore out of the defensive line and caught van der Flier high, earning himself a yellow card.
But Connacht were not just down one man, they were down two when the next scrum occurred.
With Aungier off, Matthew Burke came back into the action but under the same World Rugby rule that saw Italy lose two forwards in the same stadium in the Six Nations, Conor Oliver and skipper Jarrad Butler followed Aungier off the pitch.
All three returned when Aungier's time in the bin was up but before that Leinster scored their sixth try - and Lowe his second.
Rónan Kelleher's burst through the centre had Connacht scrambling but Ringrose's clever skip pass to Lowe allowed the winger to do what he does best.
The 29-year-old cut inside John Porch before selling Carty a dummy to score, and Sexton's conversion made it 42-8.
To their credit, Connacht replied in kind as substitute Sammy Arnold did really well to get the ball down over Leinster's try line despite the attentions of Ruddock and O'Brien.
But Ross Byrne - on for Sexton - set up Lowe for his hat-trick in the 66th minute before adding the extras himself.
The scoring wasn't finished there, either. Another Connacht replacement, Abraham Papali'i, out-manoeuvred Lowe to nab a try in the right-hand corner and, with one of the most difficult attempts he had, Carty nailed it this time.
However the last laugh went to Lowe, who raced in from the left wing to give Byrne a handy conversion to end the punishment.
