Gary Burton hit a key three-pointer with 20 seconds left in normal time that tied the game at 86-86 before skipper Mark Gledhill sealed the win in the extra period after Flyers had again got their noses in front.
The early omens weren't good for W
ellingborough as they lost guard Devon Adams to a back injury in the opening moments.
However, with Burton to the fore, they opened up a 7-0 lead before the home side responded with a 9-2 run.
Phoenix struggled from the free-throw line but in open play they were in tune as another 7-0 run put them 22-18 ahead again at the end of the first quarter.
Daniel Turiccki came to life at the start of the second period with eight points as Phoenix opened up a nine-point lead.
However, Bristol – and Jermaine Major – then woke up, with Major
hitting 11 points in an 18-4 run that ensured they led at half-time – albeit by just a point – at 45-44.
The home side kept their noses in front during a scrappy third quarter, mainly due to 13 points from star Almasi Shipei Hanada.
Wellingborough were boosted by the return of Adams but still trailed by four at 69-65 going into the final quarter.
Flyers got the jump at the start of the fourth period, opening up an eight-point lead, but 11 points from Turiccki got Phoenix back on terms.
Trailing by three points with 20 seconds left Burton hit his decisive basket to level the scores, but even then Flyers should have won it.
But Ben Kelloway missed two free-throws with four seconds left before Turiccki hit the rim with a last-gasp effort as the buzzer sounded to send the game into overtime.
Flyers opened the extra period by taking a four-point lead before Phoenix first levelled and then went three in front themselves.
A three-pointer from Banji Gellatly brought Bristol level again but Phoenix finally sealed the win through Leome Francis and finally, four points from Gledhill.
Turiccki top-scored for Phoenix with 24 points while Gledhill added 15 and Burton 13. Hanada led all scorers on the night with 30.