The English side made hard work of the win, with this Pool 3 clash still in the balance as the game entered the final 10 minutes.
However, Ryan Davis and Richard Haughton both crossed late on to secure a bonus point, meaning that a win at home to Bordeaux next week will secure a quarter-final berth.
After wasting a couple of early scoring chances, Wasps fell behind to Davide Duca's penalty after 12 minutes, but they responded almost immediately with a try from Sam Jones following a Nic Berry break.
Duca potted a second penalty to narrow the gap, but Wasps soon had their second try, Elliot Daly racing in from 40 metres to score underneath the posts.
Samuele Pace's try after the break reduced arrears to the minimum once again, but Ryan Davis kicked two penalties before scoring a late try, with winger Haughton securing a vital bonus point with the last play of the game.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.