While Bath celebrated a first win of the season at the 13th attempt in all competitions, Worcester forward Sutherland, who was in his comeback game after six weeks out injured, now faces a disciplinary hearing. Scotland host England on February 5.
The British and Irish Lion was dismissed by referee Craig Maxwell-Keys for a head-on-head challenge that forced Bath prop Will Stuart off the pitch.
But Bath, despite playing against 14 men for virtually the whole match, were made to work hard for a victory that was their first since June.
Fly-half Orlando Bailey's penalty ten minutes from time broke their Premiership duck this term, while he also added two conversions as Bath posted tries by wing Semesa Rokoduguni, centre Max Ojomoh and full-back Tom de Glanville.
Worcester, without a win from 17 previous visits to the Recreation Ground, matched them try for try as full-back Jamie Shillcock, lock Joe Batley and scrum-half Gareth Simpson touched down, with fly-half Fin Smith kicking two conversions.
Bath remain well adrift at the Premiership basement, but a long overdue success should at least lift spirits ahead of tough Heineken Champions Cup games against La Rochelle and Leinster.
Hooker Tom Doughty made his first Premiership start for Bath, packing down alongside Lewis Boyce and Stuart. Josh Bayliss returned at number eight and scrum-half Ollie Fox was also recalled, but wing Will Muir was a late withdrawal and replaced by Wales international Tom Prydie.
Sutherland returned in a Warriors side that also included former Bath prop Christian Judge, but positive Covid-19 tests meant that fly-half Billy Searle and number eight Sione Vailanu were absent.
England head coach Eddie Jones was among the crowd and the game began in dramatic fashion with Sutherland's dismissal following several video reviews made by referee Maxwell-Keys.
And Bath capitalised from their first attack after centre Jonathan Joseph's sharp midfield break helped create space out wide before Rokoduguni applied a clinical finish and Bailey converted.
Worcester, though, made a strong reply and scored their opening try just five minutes later when Shillcock's angled run saw him touch down despite the attention of two defenders.
But Bath were soon on the the front foot again, with Ojomoh scoring their second try following his midfield partner Joseph's clever kick into space, and Worcester trailed 14-5 after Bailey converted.
Bath looked to impose themselves on the contest, yet Worcester displayed admirable resilience and reduced their arrears when Batley crashed over for a close-range try, converted by Smith.
And the Warriors went in front following an impressive passage of play as centre Francois Venter's half-break sent Smith clear, before he delivered a scoring pass to his unmarked half-back partner Simpson.
Smith converted to leave Bath five points adrift, with Worcester good value for their interval advantage.
And Bath's problems were compounded six minutes into the second period when Bayliss was yellow-carded for illegally stopping a lineout drive, temporarily making it 14 versus 14.
Worcester continued to probe attacking spaces, yet Bath struck next through a 57th-minute try for De Glanville after he gathered Rokoduguni's pass and sprinted clear.
It set up a tense final quarter at 19-19 and Bailey nudged Bath back in front after 70 minutes when he booted a penalty from 35 metres, and it proved enough to thwart Worcester, who had to be content with a losing bonus-point.