Wing Josh Adams, substitute centre Wynand Olivier and former Bath lock Will Spencer struck in quick succession, underpinning Worcester's 25-19 victory that now leaves Bath chasing fourth-placed Leicester with just two regular season games remaining.
And Warriors' triumph also means bottom club Bristol effectively need a win against leaders Wasps on Sunday to avoid propping up the table and almost-certain relegation.
Fly-half Ryan Mills added two penalties and two conversions, halting Bath's eight-match winning streak against Worcester, with the visitors managing a Matt Banahan try plus four George Ford penalties and a conversion.
But they have lost crucial ground in the play-off race, with Leicester now firm favourites to join already qualified Wasps, Exeter and Saracens in next month's semi-finals.
Tighthead prop Biyi Alo made his first Premiership start for Worcester, replacing an injured Nick Schonert as a solitary switch following last week's defeat against Sale Sharks, but Bath were unchanged following victory over Leicester at Twickenham seven days ago.
British and Irish Lions assistant coaches Rob Howley and Steve Borthwick, meanwhile, were among a capacity Sixways crowd, running a final check on possible New Zealand tour candidates ahead of next Wednesday's squad announcement in London.
One of those hopefuls - Bath's Wales number eight Taulupe Faletau - was heavily involved early on, yet Worcester went closest to opening the scoring when number eight Marco Mama dived over the line, but referee Luke Pearce rightly brought play back following an earlier forward pass.
Ford kicked Bath into a 24th-minute lead when Worcester were penalised for not rolling away at a ruck, yet Worcester continued to look dangerous in attack and wing Perry Humphreys went close to a try as Bath's defence once again found itself tested.
Mills hauled the Warriors level through a penalty four minutes before half-time, only for Bath to score from their first quality attack after securing lineout possession.
England centre Jonathan Joseph found Banahan in space and he then capitalised on poor defensive work by Warriors full-back Chris Pennell before claiming his fifth Premiership touchdown of an injury-plagued season.
Ford converted from the touchline, only for Worcester to have the final say of a disappointing half when Mills kicked a penalty from almost 10 metres inside his own half, cutting Bath's lead to 10-6.
Ford opened the second-half scoring with an angled penalty, but Worcester responded eight minutes later through a try that had their England centre Ben Te'o at its attacking hub.
Te'o, billed by some as an outside chance for Lions selection, made short work of an attempted Ford tackle and sprinted clear into space before finding his midfield partner Jackson Willison in support, and Willison sent an unmarked Adams sprinting over.
Mills, though, saw his earlier kicking accuracy desert him as he missed the conversion and then an easier penalty chance from 40 metres, which he hit so poorly that it barely reached the Bath posts.
But Worcester did not let up and they scored a second try nine minutes after their opener as half-backs Mills and Francois Hougaard combined to put Olivier over just five minutes after he appeared off the bench.
Mills kicked the conversion for a five-point lead and Bath were at sixes and sevens, struggling badly to reassert their authority of the game's second quarter when they built a solid advantage.
Ford's third successful penalty 10 minutes from time gave Bath renewed hope but it was snuffed out by Spencer's touchdown that Mills converted, before another Ford penalty secured a losing bonus point for the visitors.