Newcastle, second bottom in the 10-team table, led 12-7 early on at Kingston Park, thanks mainly to a Jamie Blamire try and a converted score from Freddie Lockwood either side of Bath's Alfie Barbeary touching down.
But tries from Tom de Glanville and Will Stuart gave the visitors a six-point advantage at the interval and before Bath surged clear in the second half.
Charlie Ewels added Bath's fourth try before Scotland playmaker Finn Russell –- who also kicked five conversions –- and England back-row forward Sam Underhill went over in the final 15 minutes to earn their side a seventh league win of the season.
Elsewhere, Bristol's 54-24 win over Leicester at Welford Road meant Pat Lam's side enjoyed a 10th successive away victory in the Premiership, eclipsing Saracens' previous record of nine straight wins on the road.
This result also saw Bristol score the most points any team have ever registered against Leicester at 'fortress' Welford Road, and as much as any side have scored against the Tigers anywhere in the Premiership.
Bristol's Gabriel Oghre and Kalaveti Ravouvou scored two tries apiece in a superb attacking display by the visitors that left Bristol level on points with southwest rivals Bath.
Viliame Mata, Rich Lane also crossed Leicester's line in a first half featuring six Bristol tries, while Bernhard Janse van Rensburg went over after the break before Ravouvou wrapped things up with his second try, a superb solo score from some 60 metres out.
Sale, meanwhile, maintained their 100 percent winning record at home this season by defeating bottom-of-the-table Exeter 28-10.
Luke James and Joe Carpenter scored first-half tries before a penalty try and Jonny Hill's score gave Sale a five-point haul as Exeter suffered their eighth defeat in as many Premiership games this season.