Although they have moved a giant step closer to quarter-final qualification as Pool 4 winners, Grenoble gave director of Rugby Dai Young some second-half scares along the way.
Wasps join Bath as the only two teams still able to boast four from four at the end of the back-to-back rounds and will relish the challenges in the new year at Bayonne and home to Rugby Viadana.
But while they scored seven tries in their 47-7 Round 3 victory over Grenoble at Stade Lesdiguieres, the French side put up far stiffer resistance this time and restricted them to just a try in each half while scoring two of their own after the break.
Joe Carlisle, who ended up with 19 points from the boot from five penalty goals and both conversions, gave Wasps an early advantage before England international flanker James Haskell crossed for the only try of the half.
Elliott Daly also contributed a penalty goal for the home side but two quick-fire tries from Ratu Alipate Ratini had the Wasps alarm bells briefly ringing before Tom Varndell got a second try to see Wasps safely home and set up that potential group decider with Bayonne in the new year.