Three Bridges are still looking for their first home league win of the season after they were stunned by an injury-time header.
Eastbourne fought back from going behind early on but it took until the final moments of the game to equalise.
They broke Bridges’ hearts when Andrew Mensah nodded in Jack Battie’s deep cross to the near post.
Bridges themselves had taken a first minute lead when Lee Carney’s delicate chip found Abu Touray who slipped it home between Greg Nessling’s legs.
But the big turning point of the match came after only 18 minutes.
Elliott Romain had been cautioned 90 seconds earlier for a silly swing at Town skipper Luke Denton, who hardly helped by remaining prone until he saw the referee produce a yellow card, but then Romain seemed to be clean through on goal and got a shove by Denton that took him into Nessling.
Instead of a penalty in Bridges’ favour though, Romain was deemed to have caught Nessling unfairly and so he received a second yellow card.
Bridges continued to dominate for a while though and Touray might well have had a hat-trick on another day, but sometimes the homesters are guilty of trying to be too precise.
But with both Lee Carney and Williams Peauroux winning the midfield battle, Eastbourne were reduced to just two noteworthy efforts in the first half, Martin Grant being equal both times to deny Billy Medlock and Aaron Watson.
Grant was, however, much busier after the break as Town tried to make their numerical superiority count. Battie and Mensah (three times) were frustrated by the Bridges custodian, while Battie fired terribly wide after getting himself into a good position and Ross Sutton fired a free-kick just over the bar.
It wasn’t all one-way traffic though as Carney’s free-kick was held at the foot of the post by Nessling, while Dan Attwater needed just a touch more venom in a couple of shots at dead ball situations. And even after the late equaliser, substitute Ashley Bertrand-Kesington was only inches wide with a fierce angled drive.
Bridges: Grant, Djimah, Leach (Drinkwater 77), Attwater, Maxwell, Parsons, Peauroux, Carney, Romain, Touray (Aibangbee, Bertrand-Kesington 79), Elliott.
Unused subs: Batalidis, Aquilina.
Aerotron Man of the Match: Williams Peauroux