Wasps overcame a slow start to beat Zebre 41-27 and set up a European Champions Cup quarter-final with Leinster.
Dai Young's side will travel to Dublin at the start of April after their bonus-point success over the Italians saw them finish top of Pool Two with 22 points.
The English side were deserving winners, but Zebre more than played their part and pushed Wasps all the way in a match which was a lot tighter than many had predicted.
Two tries from Ashley Johnson and further scores from Danny Cipriani, Elliot Daly, Christian Wade and Nathan Hughes sealed an away win.
Cipriani booted four conversions and a penalty, but Wasps will have to improve on this showing if they are to make it past the last eight of Europe's premier club competition.
A one-sided encounter had been expected in Parma, but it was Zebre, who had conceded 290 points from their five matches going into this tie, that started with a bang.
Carlo Canna's eighth-minute penalty put Zebre into a surprise lead and just five minutes later it got even better.
After Wasps lost their own line-out five metres from their line, fly-half Canna spread the ball right and when Kurtley Beale jumped out of the defensive line, it allowed outside centre Mattia Bellini to make his way to the line.
Canna converted and although Cipriani got Wasps on the board with a 16th-minute penalty, Zebre deservedly extended their advantage with a penalty from scrum-half Marcello Violi.
Wasps, who had thrashed Zebre 82-14 in the return fixture, were given a boost when home hooker Oliviero Fabiani was yellow carded for a no-arms tackle on Simon McIntyre. With a man advantage, Young's side struck.
First, Johnson powered over from close range before Cipriani ghosted through a gap to dot down for two tries in quick succession.
Wasps had now woken up and there was still time for a third before the break as Daly's outside arc saw him finish in the corner past some poor Zebre tackling.
The bonus-point score arrived soon after the interval when Zebre again paid the price for poor discipline. Number eight Derick Minnie was yellow carded for infringing at a maul and Johnson soon powered over for his second.
Wade then crossed for the best score of the day, standing up the Zebre defence and sprinting clear to dive over in the corner.
Cipriani converted the first of those tries to make it 34-13 at the hour mark and, with Wasps in charge, Young removed England internationals Joe Launchbury and James Haskell from the fray with the Six Nations just around the corner.
The final quarter saw the game open up with Wasps looking for more tries and Zebre hunting a consolation. Replacement scrum-half Craig Hampson made an electric break for Wasps, but in support and with a clear run to the line ahead of him, Beale inexplicably dropped the ball.
Zebre full-back Kurt Baker then showed his opposite number how to do it by making his way to the line for another score created by Canna.
The Italian international added the extras again and there was still time for an entertaining second half to end with Hughes scoring Wasps' sixth try before Italian replacement Federico Ruzza crossed for the hosts.