Centre Alex Grove's second-half try secured the victory for Worcester, leaving bottom club Newcastle still eight points adrift with just four league games left.
Jimmy Gopperth kicked three penalties for the visitors, which was enough to secure a 9-6 advantage approaching the hour mark, but Scotland international Grove then rounded off a spell of sustained pressure and the Falcons were finished.
Gopperth's opposite number Andy Goode booted 14 points via four penalties and a conversion, his final strike denying Newcastle the consolation of a losing bonus after their hopes of a first league away triumph since February last year had already vanished.
Eleventh-placed Wasps, who host Newcastle on the regular league season's final day in early May, are not expected to gain anything from their trip to title play-off contenders Northampton tomorrow.
But Newcastle's latest defeat - their 13th from 18 Premiership starts this term - has upped the ante for remaining fixtures at home to Sale Sharks and Saracens and away against Gloucester and Wasps.
Rugby director Gary Gold, who will make way for Dean Richards next season, could not fault the effort or commitment of his players, yet Falcons lacked sufficient attacking flair or invention to seriously threaten scoring a try.
Newcastle gave loan signing Peter Stringer his Falcons debut, the Ireland international scrum-half having arrived at Kingston Park after completing a similar short-term stint with league champions Saracens.
Worcester, meanwhile, welcomed back wing Marcel Garvey and number eight Kai Horstmann after injury lay-offs as the Warriors looked to put further distance between themselves and the Premiership danger zone.
The form guide suggested a Warriors win, given they had lost just once at home in all competitions since mid-November, while Newcastle could reflect on a solitary Premiership away victory in almost two years.
Conditions were perfect for an open, running game, yet Newcastle arrived with so much at stake that for them it was all about winning, pure and simple.
Gopperth sent a rushed early drop-goal shot wide of the Worcester posts, but with both sides opting for sustained kicking strategies, clear-cut attacking opportunities were few and far between.
Defences also cancelled each other out, especially in a congested midfield area, yet Newcastle secured enough of a territorial advantage for Gopperth to kick them ahead after 13 minutes.
Neither side could get a grip on the contest, not helped by increasingly wayward and largely pointless kicking that merely gifted possession to the other team.
There was a chronic lack of confidence and imagination displayed in attack, yet Newcastle would have been far happier than their hosts as half-time approached.
Goode landed an equalising penalty just before the interval, but the Falcons finished a dire opening 40 metres with a degree of territorial control and feeling they could probably push on and secure a priceless away triumph.
Referee JP Doyle's half-time whistle could not come soon enough for Worcester, with the Warriors looking a pale shadow of the side that had beaten Saracens and Gloucester at home in the Premiership since Christmas.
Worcester, it is safe to presume, would have received an interval rocket from their head coach Richard Hill, but it was Gopperth who made the first notable contribution after the break.
The prolific marksman found his range from 48 metres to inch Newcastle back in front, although there were signs of Worcester's forwards stirring into life.
And some impressive work by the home pack ended with Newcastle infringing, allowing Goode an easy penalty chance that he accepted to make it 6-6.
Gopperth, though, restored Newcastle's advantage by completing his penalty hat-trick, and when Goode matched his achievement shortly afterwards following a slashing break by Warriors wing Miles Benjamin, the game was tied again entering its final quarter.
Worcester were far more dangerous with ball in hand than they had been in the first half, looking to find Benjamin and Garvey, who enjoyed increasing amounts of room.
And it came as no surprise when Grove crossed 15 minutes from time, his touchdown ending a prolonged spell around Newcastle's 22 that ultimately cracked open Falcons' well-organised defence.
Goode converted and then slotted his fourth penalty just a minute from time, leaving the prospect of Newcastle playing Championship rugby next season looking an increasingly likely one.
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