The home side made a blistering start and should have won far more comfortably but they failed to take advantage of all their territory and possession to allow the Warriors to remain in the game.
Wasps had the more creative players with Joe Simpson impressing but the Warriors could have sneaked it, despite once again showing limited attacking firepower.
Wasps started strongly with a try after only three minutes. Billy Vunipola and Joe Launchbury made big inroads into the Worcester defence and good ball retention saw prop Simon McIntyre drive over for the try which Stephen Jones converted.
Worcester then had their first opportunity for points but Andy Goode failed to take it as his 35-metre penalty attempt rebounded back off a post.
Back came Wasps to put the visitors' defence under sustained pressure in their own 22 and when the Warriors were offside, Jones made no mistake with an angled penalty to give his side a 10-point advantage.
After that bright opening, the second quarter of the game was a huge disappointment as both sides made frequent unforced errors which prevented any real flow to the game. There were frequent turnovers as the score deservedly remained at 10-0 to the home side at the interval.
Early in the second half, a handling error by Andrea Masi allowed Worcester a position in the Wasps' half and when the hosts were penalised, a Goode penalty gave Warriors their first points.
Almost immediately Jones was presented with a chance to nullify that score but his 45-metre penalty attempt sailed narrowly wide.
With half an hour remaining, Goode reduced the arrears to only four when he fired over a splendid drop-goal from close on 50 metres.
Stung by the two penalties, Wasps resumed their earlier dominance with Launchbury and McIntyre again to the fore with their driving runs. They should have gone further ahead when a clever chip ahead from Simpson should have resulted in a try for Christian Wade but the wing knocked on with the line at his mercy.
Jones missed another angled penalty for the Wasps, allowing the Warriors the possibility of an unlikely win. Inventive play by Paul Hodgson and David Lemi put the visitors into the Wasps' 22 but Aleki Lutui knocked on and the home side were able to relieve the pressure.
With three minutes to go, Simpson made the best break of the game, with a sniping run from a ruck on halfway but the supporting Chris Bell was hauled down narrowly short.
This allowed Warriors one final chance but Jon Clarke failed to collect a Goode cross-kick for the winning try before the Wasps withstood four minutes of huge pressure to hang on for a nail-biting win.
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