Warriors had to settle for a losing bonus point after another frustrating afternoon in the rain at Sixways.
An opportunist second half try from Nick David and eight points from Jamie Shillcock’s left boot led the fightback but Warriors were left chasing the game after Wasps crossed twice before the break.
Warriors dominated long periods of that first half but had only a penalty from Shillcock to show for their efforts while Wasps made the most of their limited attacking opportunities.
But Warriors rolled up their sleeves in the second half and had Wasps rattled with a dominant scrum – with the replacement front rows all making their presence felt – and some powerful ball carrying.
David’s try, after he and Michael Heaney had kicked ahead, came shortly after Wasps had opened up a 14-points lead, and produced a nail-biting final quarter.
Shillcock, who had an assured game at fly-half, reduced the deficit to four points with a penalty 12 minutes from time but the key moment came seven minutes later when Wasps held up a driving lineout after Shillcock had kicked a penalty to the corner.
Steady rain and numbing cold made for miserable conditions and largely shaped the match with both sides making plenty of unforced errors.
Warriors drew first blood when Shillcock landed a penalty which rewarded a period of sustained pressure but it could easily have been more.
Shillcock had found Perry Humphreys with an inch-perfect crossfield kick. Humphreys was unable to hold on but appeared to be nudged by a Wasps defender before he got to the ball.
The lead lasted only four minutes as Wasps kicked a penalty to touch on the 22, won the lineout and launched a series of pick-and-go attacks which led to James Gaskell going over near the posts.
Shillcock continued to put Warriors into promising positions with some astute tactical kicking and he came close to reducing the deficit when a long-range penalty attempt from halfway smacked against the right post and bounced out.
Instead Wasps increased their advantage just before the break when number eight Tom Willis stepped out of two tackles and crossed for a try that came from nothing.
Jimmy Gopperth levered over the conversion from the touchline to give a half-time scoreline that did not reflect possession or territory during the first period.
Warriors continued to press in the second half but it was Charlie Atkinson, Wasps’ fly-half, who scored the next points with a 59th minute penalty.
The rest of the game was dominated by Warriors who were given a huge lift when David wriggled free on the left, threaded a grubber kick through the advancing defence and was on hand to dot down after the pacy Heaney toe-poked the ball on.
But, despite further pressure, Wasps held on , grimly at times, to edge a tight contest.
Warriors | 15 Chris Pennell, 14 Perry Humphreys (Morris 41), 13 Francois Venter, 12 Ashley Beck, 11 Nick David, 10 Jamie Shillcock, 9 Gareth Simpson (Heaney 53), 1 Ethan Waller (Thomas 61), 2 Isaac Miller (Cutting 61), 3 Nick Schonert (Palframan 53), 4 Graham Kitchener (Kitchener 53), 5 Justin Clegg, 6 Ted Hill (C), 7 Matt Kvesic, 8 Cornell du Preez.
Replacements | 16 Beck Cutting, 17 Marc Thomas, 18 Richard Palframan, 19 Andrew Kitchener, 20 GJ van Velze, 21 Michael Heaney, 22 Fin Smith, 23 Oli Morris.
11m | Shillcock pen 3-0
15m | Gaskell try 3-5
16m | Gopperth con 3-7
36m | Willis try 3-12
37m | Gopperth con 3-14
59m | Atkinson pen 3-17
61m | David try 8-17
62m | Shillcock con 10-17
68m | Shillcock pen 13-17