Wasps recovered from a sluggish start to secure a bonus-point 41-27 success over Italian side Zebre on Sunday and finish top of their European Champions Cup pool, earning themselves a trip to Leinster in the quarter-finals.
Two tries from Ashley Johnson and further touchdowns from Danny Cipriani, Elliot Daly, Christian Wade and Nathan Hughes powered Wasps to victory.
Defending champions Saracens will face Glasgow at Allianz Park in the last eight with the victors playing the winners of the tie between Munster and Toulouse.
Should Wasps progress to the semi-finals, Dai Young’s side will come up against either Clermont Auvergne or Toulon.
Harlequins, meanwhile, crashed out of the European Challenge Cup after suffering a 27-17 defeat at Top 14 outfit Stade Francais.
Mat Luamanu, Marland Yarde and James Chisholm crossed the line for the visitors, although it proved insufficient for Quins, who reached the final of the competition last season.