Hill's team have not won in the Premiership since they beat relegation candidates London Welsh just before Christmas. They suffered the double blow of a last-gasp loss to Gloucester last Friday and seeing full-back Errie Claassens sent off.
But Hill said: "It is vital we keep the faith and know that if we keep playing and working hard then the win we all crave will come. It would be fantastic to record a good win in front of our fans, and the players have been working extremely hard."
He added: "Far from being down, recent events have only galvanised our squad. I watched Wasps play against Gloucester at home recently when they performed very well, and they are undoubtedly a talented team that plays with a lot of width."
Chris Pennell will replace the suspended Claassens, while Wasps are without prolific try-scorer Christian Wade through injury as they look to bounce back from a 30-19 defeat against London Irish last time out.
"We didn't play well, we weren't up to scratch in defence and we didn't retain the ball well enough," said Wasps lock Marco Wentzel, reflecting on the Irish defeat.
"That wasn't a reflection of what this group of people are capable of. There are a lot of guys who have not been that pleased this week, which isn't necessarily a bad thing. There are not many sides that go up to Sixways on a Friday night and come away with a win. If we are not fully on our game, then we are going to struggle."
Wasps could go third if they post a bonus point success, but that is also the target for Gloucester, who visit west country rivals Bath. Gloucester are boosted by the return of fit-again England international Freddie Burns, who reclaims their number 10 shirt, while Mike Tindall skippers the side against his former club.
Bath, currently seven points adrift of the play-off zone, make four changes from the side edged out by Northampton last weekend, with international props Paul James and David Wilson among those called up.
In Saturday's action, leaders Harlequins host Exeter, Leicester entertain bottom club Sale Sharks and London Irish head to Northampton. And London Welsh, who face a disciplinary hearing early next week surrounding nine ineligible Premiership appearances made by Tyson Keats - they could land a sizeable points deduction - visit Saracens on Sunday.