A well-worked Paul Hill try had given the black, green and gold a 10-3 lead early in the second half, but that only served to sting Newcastle into action.
Adam Radwan responded with a score almost immediately, and Chidera Obonna grabbed what proved to be the winning try 18 minutes from time.
It was joy for the 1,750 home fans that were allowed in to watch the game following the easing of government restrictions earlier in the day.
But for Saints it was a second successive defeat, leaving them 11 points behind fourth-placed Harlequins with just three Gallagher Premiership games to go.
Chris Boyd's side will now have a weekend off before welcoming Wasps to Franklin's Gardens, where approximately 4,000 Saints supporters are expected to be in attendance.
They would have hoped to head to that home game with play-off hopes intact, but Newcastle ended that dream.
Saints did have a chance to build a platform early on at Kingston Park thanks to a scrum penalty, but James Grayson was unable to find touch and instead it was the Falcons who took charge.
The hosts did lose a lineout deep in Saints territory but another error gave them possession back, allowing Falcons to apply the squeeze again.
Saints held out but they were giving away far too many penalties, denying them any sort of field position.
Falcons kept flying forward and the pressure told as Tom James was sent to the sin bin for a deliberate knock-on in the tackle.
But Newcastle evened the numbers up within three minutes as Callum Chick was also yellow carded for a deliberate knock-on.
It took Saints more than 20 minutes to get any sort of possession in the Falcons half and when they did, David Ribbans was smashed by two Newcastle players, forcing a knock-on.
Neither side was really able to gather any sort of momentum, with referee Matthew Carley jokingly telling the players 'we can't have 0-0, boys'.
Grayson showed he was listening to the man in the middle as he stepped up to slot a penalty three minutes before half-time, finally breaking the deadlock.
But Newcastle responded with the clock in the red as Brett Connon notched a penalty to level the scores after a first half that produced so much huff and puff but so few points.
Saints started the second half on the front foot, applying plenty of pressure, but the Falcons defence held firm.
Eventually though, the away side found a way through.
Teimana Harrison and Lewis Ludlam carried with real vigour, laying the foundation for Grayson, whose tidy offload allowed the rampaging prop Hill to score.
Grayson converted and Saints had a seven-point lead 10 minutes into the second half.
Newcastle were straight back at the door but they looked to have let Saints off the hook when they fluffed a lineout deep in away territory.
However, Tommy Freeman couldn't gather, knocking on to give the hosts a scrum, and they used it well, sending wing Radwan in out wide.
Connon kicked the conversion from the touchline, levelling the scores in the process.
Saints had a chance to respond when they won a penalty inside the Newcastle half, but Grayson missed touch to give Falcons possession back.
With 20 minutes to go, the match was very much in the balance but Falcons took hold as they shoved Saints off the ball at the scrum and worked it wide for Obonna to score.
Connon missed the conversion to leave the gap at five points and Grayson soon had a chance to cut the gap with a penalty, but he sent his effort wide.
He didn't have to wait long for another, much easier, chance though, as Fraser Dingwall found himself trapped inside his own half, allowing Falcons to win a penalty.
Connon easily kicked from in front of his own posts to put the game to bed and take Saints out of losing bonus point territory.
Newcastle Falcons: Penny (Hodgson 53); Radwan, Orlando, Burrell, Wacokecoke (Obonna 41); Connon, Shreuder (Stuart 67); Brocklebank (Cooper 70), McGuigan (Cooper 70), Tampin (Ah You 53); Peterson (van der Walt 60), Robinson; Welsh (Fearns 53), Wilson (c), Chick.
Saints: Furbank; Sleightholme (Collins 52), Proctor, Hutchinson (Dingwall 63), Freeman; Grayson, James (Taylor 63); Waller (cc) (Auterac 60), Matavesi (Haywood 60), Hill (Painter 57); Ribbans, Ratuniyarawa (Coles 57); Wood (Adendorff 66), Ludlam (cc), Harrison.
Referee: Matthew Carley