The Warriors' run of five successive league defeats deservedly ended after first-half tries from Chris Pennell and David Lemi underpinned an impressive performance at Sixways.
Worcester effectively ended any lingering relegation fears by moving 13 points above bottom club Sale Sharks with just five games left, as number eight Blair Cowan's 60th-minute touchdown left Wasps reeling before scrum-half Jonny Arr's close-range effort secured a first bonus point Premiership victory for five months.
Fly-half Andy Goode chipped in with a penalty and conversion before going off injured, while his replacement Danny Gray added two conversions to nullify touchdowns by Wasps hooker Rhys Thomas, flanker Ashley Johnson and substitute Jack Wallace.
Wasps, in fifth place before kick-off, were left to ponder a second Premiership reversal of the week after they lost against London Irish last Sunday, despite fly-half Nicky Robinson keeping them in touch through two penalties and a conversion.
Ultimately, though, Worcester were too organised and too aggressive at the contact area for their visitors, while also displaying some impressive finishing power.