A blistering opening quarter-of-an hour, that saw Gareth Thomas score, proved enough to win a scrappy affair while Jean-Baptiste Elissalde converted and added four penalties.
Wasps responded with a try from Raphael Ibanez and three kicks from England hopeful Mark Van Gisbergen.
Cardiff Blues are facing disappointment after Perpignan clinched a priceless 21-3 victory at the Arms Park.
The Blues' quarter-final hopes now hinge on them beating Leeds at Headingley next Sunday - but that still might not be enough.
Perpignan will finish top of Pool Two if they defeat Italian minnows Calvisano in their final group game, leaving Cardiff to scrap for one of two best runner-up spots with potential rivals like European heavyweights Munster, Leinster and Stade Francais.
Centre Jean-Philippe Grandclaude and substitute David Marty scored tries in each half, while goal-kicker Nicolas Laharrague recovered from a shaky start to boot three penalties and a conversion. Cardiff's only reply was an early penalty from fly-half Nick MacLeod.
Edinburgh Gunners threw a spanner in the Welsh works at Murrayfield to scupper the Scarlets' quest to sneak into the knockout phase with a 33-32 win.
The Gunners came up with the goods to keep alive with a potent display which yielded a four-try bonus point before the interval - and there was no way back for Llanelli in spite of a valiant late fightback.
Matt Mustchin, Andrew Kelly, Mike Blair, Hugo Southwell and Francisco Leonelli Morey scored the tries that put the Scots in charge but Llanelli staged an amazing flourish with tries by Lee Byrne, Alix Popham and Tal Selley, the latter two converted by Mike Hercus - however it was too little too late.
Neath-Swansea Ospreys earned a morale-boosting if hollow 26-12 victory over Clermont Auvergne thanks to 16 points from the boot of full-back Adrian Cashmore.
With both Pool 3 sides already out of quarter-final contention the match was fairly meaningless, but the win was important for the Ospreys because it ended a four-match losing run.
Richard Mustoe and Steffan Terblanche scored the Ospreys' tries and they travel to Stade Francais next week hoping to achieve a rare double over the Paris side.
Leinster's hopes of making the last eight remained alive as Brian O'Driscoll scored two tries in his first 80 minutes of rugby since June in the 46-22 win over Glasgow.
The victory keeps the Irish province on course for one of two best-placed runners-up spots, but they will need to garner at least four points from next Sunday's trip to Pool Five leaders Bath to book a quarter-final berth.
Leinster did most of the damage in the first half - Cameron Jowitt (2), Shane Horgan, Girvan Dempsey and Felipe Contepomi all crossed in the first 40 minutes.
O'Driscoll grabbed his brace late in the second half, with Denis Hickie adding the eighth in injury-time.
Leeds Tykes' clash with Ghial Calvisano was postponed due to a frozen pitch.
Leeds coach Darryl Powell said: "We really wanted the game to go ahead with a big match against Cardiff Blues next weekend. However we agreed with the decision not to play as the safety of the players is the most important thing."