Giant centre Matt Banahan then crashed through the Wasps defence, ably assisted by Dan Hipkiss, to score the first try of the match for Bath.
At 10-3 up, Nick Robinson added another penalty for Wasps, putting the half-time score at 10-6.
Tom Biggs beat Christian Wade in a foot race early in the second half, planting the ball under the posts to extend Bath's lead to 20-6.
Wasps pulled one back shortly after, with Tom Varndell rising highest to claim a kick, touching down in the left-hand corner.
Kyle Eastmond added Bath's third, showing nimble feet to evade seven tackles and dart under the posts to put Bath 27-13 up.
Christian Wade continued his scoring form with a break-away try from nothing, but it was not enough for Wasps as Bath held out to seal a 30-23 victory.