Ger Rowe celebrated his Irish U23 call-up by claiming his first goal at the Carlisle Grounds.
Bray's win lifted them up to fifth in the table for 24 hours at the very least.
It was Ramblers fifth away defeat of the campaign at they finished with ten men as Alan Kearney was stretchered off in the 86th minute.
The game’s only goal came in the 63rd minute after throw-out by Bray goalkeeper Chris O'Connor led to Paddy Kavanagh being fouled by Kevin Murray.
Alan Cawley whipped in a quick free and Ger Rowe got away form his marker to steer a brilliant ten-yard header into the roof of the net although Cobh’s James McCarthy managed to get his fingertips to the ball.
But the Seagulls had a major let-off in the 74th minute when substitute Gareth Cummins beat the offside trap and lofted a 30-yard effort the advancing Chris O'Connor only for the ball to bounce back off the crossbar.
Kieran O'Reilly followed up but with Derek Foran back on the goal-line, his shot went high and wide.
The Munster had started the game the stronger side and were unlucky not to take the lead.
After James McCarthy smothered a shot from Ger Rowe the visitors broke straight away with Kieran O'Reilly getting clear along the right wing. His cross was deflected to the in-rushing John Kearney only for Chris O'Connor to make a point-blank save.
Despite Ramblers hard work, Wanderers were only denied a 25th minute lead by the crossbar when Paddy Kavanagh’s opportunist 20-yard drive cannoned off the bar and over.
Bray brought on Paul Dunphy at half-time and the substitution nearly paid dividends within four minutes of the re-start when he released Bray captain Colm Tresson whose 10-yard effort rebounded back off the upright.
Soon after at the other end, a poor O'Connor goal-kick was headed back allowing O'Reilly to break clear, but his clever 25-yard lob dropped beyond the bar above the stranded Australian.
Bray Wanderers: O'Connor; Pender, Doherty, Foran, Cronin; Whelan (Dunphy half time), Tresson, Cawley, Duggan; Kavanagh, Rowe.
Cobh Ramblers: James McCarthy; Carey, Murray, Guthrie, Brian McCarthy; Mulconry, John Kearney (Cambridge 81 mins), Alan Kearney, Meade; O'Reilly (O'Neill 77 mins), Conor Meade (Cummins 69 mins).
Referee: Mark Gough (Limerick).
