Wasps' England winger Tom Voyce played a decisive role in sinking his former club, scoring an early interception try – while Ed Thrower kicked 11 points, and fly-half James Brooks slotted a late drop-goal to seal the deal.
The win leaves Wasps neatly tucked in behind the early Premiership pace-setters before a fortnight's break for Heineken Cup action.
Bath gave it everything, but three Olly Barkley penalties and a late converted try by substitute Chris Malone saw them fall narrowly short.
Wasps, following early-season defeats against Saracens and Sale Sharks, are slowly moving through the gears – even though they have a debilitating injury list.
Lawrence Dallaglio's men will need to make another step up in the Heineken Cup arena, yet their priceless ability to win tight games once again surfaced in front of a 10,500 league record crowd for Bath.
Barkley was at the heart of Bath's best attacking moments, and their forwards were predictably robust. Wasps, though, won the key battles when it mattered.
Wasps, the only visiting team to win a league game at Bath last season, arrived in the West Country without five injured English internationals after scrum-half Matt Dawson (hamstring) joined Josh Lewsey, Stuart Abbott, Simon Shaw and Fraser Waters as high-profile absentees.
Prop Will Green returned after recovering from a shoulder problem, though, while Bath retained the team which drew 16-16 with Leicester last weekend.
Wasps made a dream start – thanks to Bath's generosity – when a grateful Voyce sprinted over from 60 metres.
Bath dominated possession from the kick-off, but fullback Lee Best's intended pass to wing Brendon Daniel was intercepted by Voyce who emphatically took his chance.
Thrower's conversion put Wasps 7-0 up inside two minutes, and given that the last two games between the clubs – including the Zurich Premiership final five months ago – had produced a total of only 32 points, Bath could feel deeply frustrated.
Barkley narrowed the gap with a 16th-minute penalty, and there was little to choose between the teams after an aggressively-fought opening quarter.
Bath, determined to build on a mighty performance by their pack at Leicester, displayed distinct signs of gaining forward supremacy. But Thrower's opening penalty success restored the visitors' seven-point advantage.
Barkley booted his second penalty eight minutes before half-time, and home coach John Connolly made an immediate substitution – replacing tighthead prop Duncan Bell with England international Matt Stevens.
Bath pushed for a score as the interval approached, but great defensive work from Dallaglio snuffed out a try-scoring opportunity when Barkley's clever kick almost found centre Mike Tindall.
It was a predictable war of attrition, yet Bath should have gone ahead when scrum-half Martyn Wood's rolling kick into space bounced perfectly for unmarked wing Andrew Higgins.
Higgins initially looked to have grounded the ball, but referee Steve Lander sought clarification from the televion match official. Replays showed that possession had agonisingly squirted out of Higgins' grasp, and a golden opportunity was missed as Wasps trooped off 10-6 ahead at half-time.
Thrower had two chances to extend Wasps' lead with long-range penalty kicks in rapid succession. His first attempt drifted wide, but the second unluckily bounced back off the crossbar – and Bath hurriedly cleared possession.
Both sides needed a flash of inspiration from what had developed into a stamina-sapping encounter, and injuries inevitably took their toll with Wood going off and Wasps' limping fly-half James Brooks requiring treatment on his left hamstring.
Thrower's second successful penalty edged Wasps a converted try in front at 13-6, only for Barkley to find his range from almost 50 metres and ensure an intense closing quarter.
Wood's replacement Nick Walshe, and Thrower – courtesy of a mis-directed kick by Voyce which caught Bath flat-footed – both made threatening breaks deep into the heart of opposition territory, but another Thrower penalty kept Wasps seven points clear.
Brooks' 74th-minute drop-goal made the game safe – inflicting a second home defeat of the campaign on Bath following Newcastle's triumph last month, even though Malone's late touchdown produced an exciting finale and secured a losing bonus point.
For Bath:Try: MaloneCon: BarkleyPens: Barkley 2
For London Wasps:Try: VoyceCon: ThrowerPens: Thrower 2