Coleraine began on the front foot and had already threatened the Crusaders goal before the hosts were reduced to 10 men following the dismissal of Rough.
The big Scottish defender went in heavy on Wylie in front of the dugout and referee Shane Andrews had no hesitation in producing the red card.
The visitors made full use of the extra man, opening the scoring minutes later through Wylie.
Devine, back in the starting line-up, fed the midfielder, who took one touch to control the ball before firing low past Shea Callister.
Devine went from provider to goalscorer when he doubled his side's lead with a wonderful strike from distance, giving the Crusaders goalkeeper no chance.
It was 3-0 just before the break when Matthew Shevlin and Ben Doherty combined to present a chance for Cooper, who swept the ball home from 12 yards for his fifth of the season.
The Bannsiders stretched their lead seven minutes after the restart, the unfortunate Blaney putting through his own goal after Finn Tonks' corner deceived everyone in the worsening conditions.
And there was still time for Brooks - the striker who left Crusaders in a big money move in the summer - to net his first goal for his new club, getting on the end of a Lewis McGregor cross to score in the dying minutes.
It's now four wins in a row for the table toppers and a fourth loss in succession for the Crues.