Bath kept their hopes of domestic glory alive with a decisive second-half comeback as they inflicted on Newcastle a first league defeat since November.
Title-challengers Leicester and Harlequins have both seen unbeaten away runs erased at Kingston Park recently but, with their season on the brink of collapsed, Bath rallied to regain their place in the top four.
Mickey Young had created one and scored the other as the Falcons established a commanding 14-0 lead at half-time.
But with their play-off ambitions wavering, Bath fought back after the break with tries from Michael Claassens and Shontayne Hape.
And, after a torrid day in front of goal for Bath's kickers, Ryan Davis converted a penalty to edge out the Falcons 15-14.
Before Will Greenwood started breaking down moves off the field, he was doing the business on it - and no match better illustrated the type of marauding centre he was than in a virtuoso performance against Wales.