Zebre, who have won only one game this season and just two in 28 in the last year, dominated the early exchanges and deservedly built a 10-point advantage.
But Oliviero Fabiani was sin-binned after 30 minutes and Wasps scored three tries in the remainder of the half.
Derek Minnie was also carded after the break as Wasps added three more tries.
Wasps, the 2004 and 2007 champions, began the final round of matches in second place, a point behind Connacht, but were confident of a comfortable victory against the minnows they had thrashed 82-14 in the reverse fixture in October.
But in the opening half-an-hour, they could only produce a Danny Cipriani penalty as all the pressure came from the hosts, who scored the first try when Mattia Bellini breached a gap in the defence.
However, Zebre were left a man down when Fabiani was shown the yellow card for a no-arms tackle and Ashley Johnson soon powered over from close range.
Cipriani ghosted through the challenges following a driving maul and the ball was worked wide for Elliot Daly to add a third.
As the home side tired, Minnie was sin-binned for an infringement at a maul and Johnson added a second, with Christian Wade also getting on the scoresheet when he scampered through in the corner after some fleet-footed work on the touchline.
Nathan Hughes had been on the field only a matter of moments when he completed the scoring for the visitors, with Connacht missing out on the last eight after they were beaten 19-10 by Toulouse.
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Wasps secured top spot in their pool and a Champions Cup quarter-final at Leinster after coming back from behind to see off bottom side Zebre in Italy.