Leeds Carnegie slumped to their seventh successive Aviva Premiership Rugby defeat as Wasps returned to winning ways at Headingley.
Scrum-half Joe Simpson scored a superb try five minutes before the break to help the visitors into a slender 7-3 interval lead following a poor opening 40 minutes. Flanker Tom Rees burrowed his way over for a second shortly after the restart and although Leeds hit back through Luther Burrell, they could not find a way back.
It was a much-needed victory for Wasps following their dismal 37-10 loss at home to Northampton last weekend, but the result left Leeds bottom of the table and without even a losing bonus point. The hosts created precious little against an understrength Wasps side missing Simon Shaw, Dave Walder, Ben Jacobs, Rikki Flutey and Richard Haughton.
Leeds, without England duo Steve Thompson and Hendre Fourie, looked to begin strongly but Wasps had the first scoring opportunity of the match. In the ninth minute, Mark Van Gisbergen, pressed into action at fly-half, sent a penalty wide of the posts and Leeds began to gain a foothold on proceedings.
They struggled to fashion genuine try-scoring opportunities and instead looked to their forward power through the middle. Midway through the half, Wasps forward Joe Worsley sustained a nose injury in a collision and Serge Betsen entered the fray as a blood replacement.
Leeds fly-half Ceiron Thomas, pressed into action at full-back, then missed a penalty as both sides struggled with kicks and in open play. Shortly after the half-hour mark, Leeds engineered an opening down the left flank but Wasps stood firm to deny them a way through.
Having weathered Leeds' pressure, Wasps hit the hosts with a sucker-punch in the 35th minute when Simpson took the ball from the back of a scrum and raced from inside his own half to cross the line. It was a superb effort and comfortably converted by Van Gisbergen before Thomas got Leeds off the mark with a penalty on the stroke of half-time.
Six minutes after the restart, Wasps claimed their second try when Simpson's short offload found Rees and he burrowed over from close range. Van Gisbergen converted and then missed a penalty that would have given his side further breathing space.
However, shortly before the hour mark Leeds threw themselves a lifeline when Scott Mathie and Henry Fa'afili combined to send Burrell scampering clear. Thomas' conversion attempt rebounded off a post and a penalty from Van Gisbergen kept the scoreboard ticking over for Wasps, who withstood a spirited, but ultimately fruitless, late rally from Leeds.