Bridges were left cursing after they allowed a two-goal lead to slip, and they were further disappointed when they heard that relegation rivals Chatham had themselves come back from two down in their game!
Bridges were clearly the better side in the opening stages and they took a 15th minute lead when Alex Rose's cross was touched by Dominic Toussaint into the path of Abu Touray, who had already had one effort ruled out for offside and had the Molesey contingent crying out for a similar decision this time too!
Tony Garrod dragged a shot wide after some excellent footwork to create the chance for himself, and Molesey at last produced a shot of note midway through the first half with a good effort on the turn by Dre Grobler.
And the half ended with Martin Grant turning away a solid drive by Rhys Paul and then making a great flying save to keep out Grobler's volley.
Bridges for once looked sharp at the start of a second half with Garrod having a shot charged down from Touray's low cross.
Rose had been involved in the build-up to that effort, and after 54 minutes he was involved again with a lovely long ball over the top that Garrod took in his stride before lobbing keeper Liam Allen.
Grobler burst through but was denied by Grant, but after 65 minutes Joe Nwoko set up Grobler for a nicely-placed finish.
Ashley Lodge then shot wide following another set up by Nwoko, who was getting into the swing of the game after an anonymous first half.
Grant tipped over a great effort from Ross Chalke, who then headed over as the resulting corner was delivered by Craig Lewington.
But with just three minutes left, Chalke got his reward with an excellent header as Nwoko provided the perfect cross from the left.
More disappointment for Paul Faili and co, but the team insists it will fight on.
Bridges: Grant, Mobsby, Rose, Grant, Odofin, Lansdale, Toussaint (Allen-Djilali 72), Hall, Garrod, Touray, Fender (Pierre 79).
Unused subs: Wilson, Benz-Salomon
Aerotron Man of the Match: Martin Grant