Despite leaving a clutch of returning international stars on the substitutes' bench, Warren Gatland's side scored tries through Matt Dawson and ebullient centre Ayoola Erinle in the first half and looked to have far too much for the Sharks, who were a shambles in an error-ridden opening period.
But despite being 24-3 down at half-time, the Sharks amazingly fought back in a bad-tempered second half and, after scores by Sebastien Chabal and Steve Hanley, twice, could have grabbed a draw.
But American fly-half Mike Hercus missed the crucial conversion two minutes from the end and the London outfit survived.
Sale, who decided to play their internationals from the first whistle, have now lost three games running and with a tough schedule looming, their campaign looks to be grinding to a halt.
Even more alarming for the Sharks was the poor all-round performance of their fly-half and attacking pivot Charlie Hodgson, who went off injured early in the second half having given up his kicking duties to Hercus and being guilty of missing a series of tackles.
Sharks chief executive Niels de Vos claimed prior to kick-off that the forthcoming six weeks were the most important in his club's recent history.
But his men struggled to get out of their own half in the opening 20 minutes as the dominant visitors established an 11-point lead.
After Mark Van Gisbergen knocked over a penalty, Wasps extended their advantage with the game's opening try in the ninth minute.
A succession of missed tackles allowed Paul Sackey and then Tom Voyce to penetrate the Sale defence, and after a number of phases, England international Dawson sniped over from two yards for his fifth score of the season. Van Gisbergen missed a simple conversion.
The South African full-back found his target from the touchline with his second penalty to make it 11-0.
Sale were their own worst enemies in the first half, conceding a raft of penalties and missing first-up tackles.
Hodgson, meanwhile, continued his poor recent goal-kicking run by missing two simple kicks.
The sides were reduced to 14 men apiece when first Sale's Jason White and the visitors' Lawrence Dallaglio – much to the crowd's pleasure – received yellow cards within minutes of each other.
Hodgson, whose confidence looked visibly drained, gave Hercus the kicking duties and the American responded by notching his side's first points from the boot.
Van Gisbergen replied with two of his own, and Wasps piled on the agony in the dying stages of the half when Erinle, remarkably overlooked by England given their well-documented midfield problems, easily skirted Hercus on the left wing to breeze majestically over for his ninth try of the campaign.
Sale dominated the feisty early exchanges in the second period and managed to notch a penalty through Hercus.
After seeing Hodgson forced off, they gained the whip hand when Tim Payne was sin-binned after 52 minutes.
The crowd were given a lift following a bout of fisticuffs between wings Hanley and Sackey before crowd favourite Chabal narrowed the gap further when he barged over from two yards after a barrage of pressure. Hercus converted.
The try prompted Wasps to draft on their artillery from the bench and they extended the lead through Alex King's penalty.
With five minutes left, an ambitious mis-pass by Mark Cueto was picked up by Hanley, who galloped over from 40 yards along the touchline to ground.
Hercus converted and Hanley then repeated the dose with a mazy 50-yard run to give Sale hope of stealing a draw.
But Hercus missed the resulting conversion and a nervous Wasps side edged the win.