With Dundalk dropping points in Sligo, City could have closed the gap to only two points but despite dominating a one-sided second half, they couldn’t add to Garry Buckley’s 50th-minute equaliser, despite playing against 10 men for an hour.
Gareth McDonagh gave the visiting side the ideal start when he struck in the 15th minute from Bray’s first attack of the game.
Ismahil Akinade ran at the Cork defence and when he lost possession, the ball broke kindly to McDonagh, who turned and swivelled before burying a low shot past Mark McNulty.
City were almost level within four minutes but Stephen McGuinness made a great stop to tip Buckley’s shot over the crossbar.
After looking so comfortable against an out-of-sorts Cork side, Bray were guilty of shooting themselves in the foot in the 32nd minute when Michael Barker dived in needlessly on John Dunleavy on the right touchline and the Bray right-back received a straight red card from referee David McKeon.
Alan Mathews’ side were always going to struggle with 10 men and Morrison’s header came back off the crossbar from the resulting free-kick from Billy Dennehy following the sending off.
The home side were no doubt given a rollicking from boss John Caulfield at half-time and the Cork manager introduced Danny Morrissey for the ineffective Cillian Morrison at the break.
The home side were level in the 50th minute when Billy Dennehy picked out O’Sullivan in the box and his neat lay-off was inch perfect for the inrushing Buckley, who buried his shot from 15 yards giving McGuinness no chance in the Bray goal.
It was all City now and Danny Morrissey should have done better with two chances in quick succession but failed to hit the target with either, before McGuinness made a good stop to deny O’Sullivan.
Substitute Philly Hughes should have put his side back in front on the hour mark following a terrible kick from McNulty but Dunleavy got back to clear off the line as the ball was about to trickle over.
McGuinness got down well to stop Danny Morrissey’s glancing header before Adam Mitchell blocked Gearoid Morrissey’s shot from 10 yards 12 minutes from time as the home side piled on the pressure in search of the winner.
Danny Morrissey headed straight at McGuinness and Buckley side-footed over as City spurned two more opportunities in the closing 10 minutes as a resolute Bray side held on for the point to put a major dent in the home side’s title hopes.
McNulty; Lenihan, Murray, D Dennehy, Dunleavy; Morrison (D Morrissey 45), G Morrissey, Buckley (O’Shea 88), Healy, B Dennehy; O’Sullivan.
McGuinness; Barker, Cooney, Mitchell, Gorman; Akinade, Kelly, Zambra, Scully, Cassidy (O’Connor 45); McDonagh (Hughes 56).
David McKeon (Dublin).