Most of the damage was done during a dominant first half display from Leo Cullen’s men, with Robbie Henshaw’s late breakaway score making it 22-3 and adding to earlier tries from Isa Nacewa and Jack Conan.
Joey Carbery’s attacking instincts from full-back earned him the man-of-the-match award, but former Leinster player Jimmy Gopperth sparked a revival from the visitors, converting Christian Wade’s try and his own effort on the hour mark.
With their lead cut to 25-17, Leinster impressively seized control again in the final quarter and replacement McFadden’s seven-pointer sealed his side’s trip to France in three weeks’ time (April 22-23), with either Clermont Auvergne or Toulon providing the semi-final opposition.
Leinster were the early aggressors in this meeting of the current GUINNESS PRO12 and Aviva Premiership leaders, and six minutes had elapsed when a 33-metre penalty from Jonathan Sexton punished Joe Launchbury’s side-entry at a maul.
After Wasps blew their first two lineout opportunities, with Nathan Hughes being turned over and the heavily-targeted Danny Cipriani passing straight into touch, they survived a Garry Ringrose-led break up the right wing.
However, strong runs from Adam Byrne and Dan Leavy got Leinster straight back into scoring range and Carbery’s brilliant skip pass released captain Nacewa for an unconverted 14th-minute try in the left corner.
A barnstorming charge form the industrious Sean O’Brien had Wasps briefly under pressure, before Dan Robson’s clever kick sent Carbery rushing back to cover in front of his posts.
Kurtley Beale provided some much-need inspiration for Wasps when he returned a Carbery kick in superb fashion, breaking over halfway and offloading for the supporting Willie le Roux but the South African blundered when losing control of the ball as he dived over the try-line.
After that 24th-minute let-off, Leinster errors saw them cough up a penalty from an attempted maul and then prop Tadhg Furlong, who was a busy figure in open play, was pinged for a tackle off the ball which Gopperth turned into three points.
However, the counter-attacking Carbery soon knifed through along with McFadden following a loose Wasps kick, and their neat interplay wide on the right released number 8 Conan for a cracking 33rd-minute score.
Sexton converted and also added the extras to Henshaw’s opportunist try which saw Devin Toner rip the ball free from a Wasps maul and Leavy, O’Brien and Sexton swiftly combined to send the centre surging over.
The rain made conditions more difficult on the resumption, with Wasps’ execution continuing to let them down. Sexton split the posts with another penalty in the 48th minute.
Five minutes later, Wade’s blistering pace earned Wasps their first try, the winger dotting down his own grubber kick to the right of the posts after Carbery, returning a kick, had been turned over.
Gopperth converted to reduce the arrears to 15 points and play became increasingly fractured, Leinster pressing twice in the 22 before Elliot Daly’s long kick downfield had Henshaw scampering back to save a potential try.
That score came from Gopperth who produced a classy finish against his former side, evading two tacklers from the edge of the 22 and converting for good measure. Suddenly, Leinster were only eight points ahead.
A sidestepping run from Ringrose almost produced the ideal response from the province, although Wasps forced a subsequent knock-on and then Wade beat Nacewa to a dangerous cross-field kick from Sexton.
In the end, Leinster’s stranglehold of territory, coupled with Wasps’ heavy defensive workload, saw the visitors give way seven minutes from time. Toner barged through to a few metres out and produced quick ruck ball for McFadden to slither over under pressure from two defenders. Sexton’s crisply-struck conversion was the final nail in the coffin.