Something had to give between two struggling teams: Exeter came into the game with the worst Premiership start and the Falcons went 581 days without a win, a run that dates back to March 2023.
Initially it looked like the hosts would fail as Chiefs got off to a great start and Feyi-Waboso completed a sweeping left-right switch in the corner after just four minutes.
Far from slumping, Newcastle dug in and after Josh Hodge missed a difficult conversion from the right touchline, they were soon in the lead.
Exeter, forced back not by quick line breaks but by their own mistakes, ended up having to defend desperately as the Falcons pondered close to the line.
In the 18th minute, Van der Walt finally managed to break through and Grayson gave the extras the lead.
With two penalties from Hodge, the Chiefs briefly regained the initiative and made it 11-7 in their favour, but indiscipline led to them conceding 13 penalties in the first hour of play.
The Falcons took the lead on Blamire’s first try after half an hour, a tap-and-drive that saw the hooker break through two tacklers from five yards out.
Exeter have been their own worst enemy all along.
Richard Capstick was shown a yellow card for going to the basket from an offside position just before half-time and although Exeter managed to shut out Newcastle during their timeout, the try seemed to be telling as the Falcons came out strong in the second period.
Blamire pushed forward for a second and when Grayson scored a drop goal from 30 yards to make it 24-11, the home fans began to believe.
However, Exeter made them sweat right until the end when Hodge finished off a full-length move and scored a brilliant conversion just down the left touchline.
But with a six-point difference, a catch-up effect as Exeter tried to make a final push from their own 22 saw the final whistle blow.