Ashley Johnson was sin-binned after just 17 seconds as Wasps couldn’t pull off an amazing comeback, drawing 20-20 as Leinster sealed a quarter-final.
Leinster top the pool as a result, with Wasps second and still waiting on other results to see if they reach the last eight.
It could have been different, with Andy Goode seeing his last-second drop-goal attempt drift wide with the win going with it.
Johnson had taken out Dave Kearney from the kick-off and was arguably fortunate to only receive a yellow card, but it gave Leinster the initiative.
With Johnson missing, Leinster scored a first try through Fergus McFadden, and they dominated both possession and territory, with a second score from Isaac Boss helping them to a 20-6 half-time lead.
Wasps turned things around in the second half, and went over on the hour through Matt Mullan.
They then drew level through Nathan Hughes, with Goode kicking well, unlike his Leinster counterpart Ian Madigan, but they couldn’t find the final score they needed.
It was a disastrous start for Wasps, who lost flanker Johnson within a minute, and they had conceded a try before they even touched the ball.
Leinster set up consecutive driving mauls, and while Wasps were able to stop them initially, the ball was then spread wide, and McFadden had plenty of space to go over on the right. Madigan converted from the touchline to make it 7-0 after just three minutes.
Wasps were shell-shocked, but they reacted well, and Goode cut the deficit with a penalty after a knock-on was collected from an offside position by the visitors.
The home side survived the remainder of Johnson’s sin-binning, with Madigan missing a first kick of the afternoon from long range, and he was off-target a couple of minutes later with a much easier effort when Ben Jacobs failed to roll away in a tackle.
A kick straight out a minute later completed a poor five minutes from Madigan, but he made up for it with some dancing feet that almost set up Leinster’s second try. Wasps showed their defensive resilience to keep Leinster out, but conceded a penalty which the inside centre slotted to make it 10-3.
Leinster were dominating possession and territory, and things got worse when Wasps lost prop Lorenzo Cittadini for ten minutes for slowing the ball down in a ruck, with Jimmy Gopperth adding three more points for the visitors while Madigan was getting some treatment.
Back down to 14, Wasps again responded well, with Goode knocking over his second penalty of the afternoon to reduce the deficit to 13-6, this time Sean Cronin was the man caught offside.
However Leinster were able to capitalise on the extra man, and Boss, on for the injured Eoin Reddan, stretched over at the back of a ruck after yet another period of possession deep inside the Wasps 22.
Madigan’s conversion made it 20-6, and Leinster were in complete control, but just before the break Wasps were given a lifeline. It came when Kane Douglas put in a needless shoulder on Johnson off the ball, and he was rightly sin-binned as a result. Goode missed the relatively simple penalty as a result, as the visitors took a 14-point lead into the break.
Leinster started the second half a man down, but it didn’t seem to make a difference early on as they got back on the front foot. A third try seemed inevitable after another charge from McFadden, but with Wasps scrambling, the visitors used an American football style block to try to crash over and were penalised.
Wasps needed something and they nearly had their first try when Tom Varndell went over on the left but it was called back for obstruction. This one was less obvious, with Luke Fitzgerald trying to tackle Hughes rather than Varndell.
To make matters worse, that play marked the end of Leinster’s numerical disadvantage as Douglas returned to action. And with him back on the pitch, Leinster could have stretched their lead but again Madigan was off-target with a penalty.
Just after the hour Wasps finally got over the line, and back to within a score thanks to Mullan. It came from a line-out five metres out, and after a number charges from the forwards, the England loosehead was just able to get the ball down over the line.
Goode’s conversion from out wide was on target and Wasps were back within a score.
Having looked dead and buried, the try seemed to spark Wasps, and they were back level with ten minutes remaining from a similar score. Again their rolling maul made ground initially before Hughes dived over the ruck to dot down.
Goode initially missed the conversion from out wide, but Leinster had charged early, and he made no mistake with his second attempt.
Leinster could have taken the win with four minutes remaining when Elliot Daly came in from the side, but again Madigan was off-target.
It was the same for Goode with time up, and Wasps now have their fingers crossed for help from elsewhere.
Tries: Mullan, Hughes
Cons: Goode 2
Pens: Goode 2
Yellow Cards: Johnson, Cittadini
Tries: McFadden, Boss
Cons: Madigan 2
Pens: Madigan, Gopperth
Yellow Card: Douglas
Wasps: 15 Rob Miller, 14 Christian Wade, 13 Elliot Daly, 12 Ben Jacobs, 11 Tom Varndell, 10 Andy Goode, 9 Joe Simpson, 8 Nathan Hughes, 7 James Haskell (c), 6 Ashley Johnson, 5 James Gaskell, 4 Bradley Davies, 3 Lorenzo Cittadini, 2 Edd Shervington, 1 Matt Mullan.
Replacements: 16 Carlo Festuccia, 17 Simon McIntyre, 18 Jake Cooper-Woolley, 19 Kearnan Myall, 20 Guy Thompson, 21 Ed Jackson, 22 Alex Lozowski, 23 Andrea Masi.
Leinster: 15 Rob Kearney, 14 Fergus McFadden, 13 Luke Fitzgerald, 12 Ian Madigan, 11 Dave Kearney, 10 Jimmy Gopperth, 9 Eoin Reddan, 8 Jamie Heaslip (c), 7 Jordi Murphy, 6 Dominic Ryan, 5 Kane Douglas, 4 Devin Toner, 3 Marty Moore, 2 Sean Cronin, 1 Michael Bent.
Replacements: 16 Richardt Strauss, 17 Jamie Hagan, 18 Tadhg Furlong, 19 Mike McCarthy, 20 Jack Conan, 21 Isaac Boss, 22 Gordon D’Arcy, 23 Darragh Fanning.