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Joe Carlisle was clinical with the boot in the first half, adding three penalties for the hosts, while James Haskell broke free to score the opening try of the match, leaving Wasps with a comfortable lead at half time.
The visitors caught Wasps sleeping shortly after the restart, allowing Ratu Ratini to score the opening points of the game for the French side.
Ratini managed to add a second, but further penalties from Carlisle and a late try from Tom Varndell ensured that the comeback was never really on for Grenoble.
The result leaves Wasps top in pool four, having won all four of their games so far in the competition.