The Falcons overtook Sarries with the win, and now lie four places and eight points away from the drop zone, with a trip to second-bottom Bath as their final regular season match.
Saracens stand one place and three points below Newcastle, still facing the mathematical possibility of relegation, but they nearly came back from the dead against a Newcastle side who made full use of their quick backs.
A first-half try from fly-half Jonny Wilkinson, converted by himself, saw the home side only three points down at the break, after veteran Australian centre Tim Horan had scored a try for the Vicarage Road side, converted by Andy Goode, who also added a penalty.
But the Falcons came out firing, and tries by England caps Jamie Noon – who was last week named Premiership Player of the Month – and Michael Stephenson put them out in front.
A penalty try in Newcastle's favour, and Wilkinson's third conversion, looked to have put the game beyond all doubt, but there was a sting in the Saracens tail.
Kiwi prop James Storey and scrum-half Kyran Bracken went over for tries the boot of Goode taking them to within four points, but despite the sin-binning of Newcastle lock Stuart Grimes, it was not meant to be.
Newcastle held out, while Saracens gained a potentially-valuable bonus point for their late exertions.
For Newcastle Falcons:Tries: Wilkinson, Noon, Stephenson, Penalty tryCons: Wilkinson 3
For Saracens:Tries: Horan, Storey, BrackenCons: Goode 2Pen: Goode