There was little answer to Bohemians' quality as Stephen Kenny's side enjoyed a comfortable passage through to the semi-finals with stunning goals from Paul Keegan and Paul McNally putting the gloss on this win.
One felt Bray, who had never beaten Bohemians in five previous cup meetings, had to get their noses in front if they were to end their visitors' unbeaten start to the season. The chance to do that came and went on six minutes as Jason Byrne, who did well to skip away from the attentions of Derek Coughlan from Phil Keogh's ball, fired a well-struck shot inches over the Bohemians crossbar.
Suitably stirred, Bohemians took a hold on the game to run up their matchwinning lead before the break. Keegan and Kevin Hunt had half chances before former Bray striker Keegan scored a stunning lead goal on 13 minutes.
Bobby Ryan, fouled by Mick Doohan, picked Keegan out from the resultant free-kick and the finish was sublime as Keegan connected with a bicycle kick to send the ball into the top right-hand corner of Matt Gregg's net.
Gregg was busy again on 34 minutes, tipping Ryan's curling free-kick over his crossbar for a corner before the winger was instrumental in Bohemians' second goal five minutes before the break.
Barry O'Connor conceded another corner as Gregg touched Mark Rutherford's looping header from Ryan's cross on to a post. Defender Paul McNally then rose unchallenged to get a header to Ryan's corner and Glen Crowe pounced just yards out to head home his ninth goal of the season.
Bray staged a revival of sorts on the resumption with Colm Tresson forcing Bayes into a diving save within three minutes.
Bohemians' hold on the game was not to be denied and Keegan saw his header over Gregg cleared off the line by Jody Lynch on 52 minutes before the win was secured with another superb goal on 66 minutes.
Bray only half cleared a free-kick in from the right by Damien Lynch. The ball broke in front of McNally who hit a stunning left-foot volley from the edge of the area through a crowd area and into the net.
Byrne hit a post at the other end shortly afterwards, but Bray's hopes of getting back into the game had long gone. Substitute Gary O'Neill added the fourth goal with a right-foot drive two minutes from time.
BRAY WANDERERS: Gregg; Britton, Lynch, Doohan, Farrell; Tresson, Gormley (Ryan 70 mins.), Keogh, Fox (Zahid 62 mins); O'Connor (Forsyth 81 mins), Byrne.
BOHEMIANS: Bayes; Lynch, Coughlan, McNally, Webb; Ryan (O'Neill 81 mins), Caffrey, Hunt, Rutherford (O'Connor 86 mins); Keegan, Crowe (Harkin 72 mins).
Referee: J Feighery (Dublin).