At Solitude, the visitors fashioned the first clear opening when PJ Morrison raced from his line to smother at the feet of Brooks, before Odhran Casey slid in with a superb last-ditch challenge to deny Finlay Thorndike with the goal gaping.
The Crues threatened again when Rory Hale was dispossessed inside the Cliftonville half, allowing Fraser Bryden’s low effort to spill into the path of Thorndike, but the home side scrambled back to clear their lines.
Just before the half-hour mark, the visitors made the breakthrough as Thorndike’s corner sparked chaos in the penalty area, with Ryan Curran inadvertently heading into his own net.
Into first-half stoppage time, Casey picked out Joe Sheridan at the back post, and his cut-back found Eric McWoods, who looked certain to score until Jordan Forsythe produced a vital goal-line clearance.
Midway through the second half, Jack Keaney almost levelled after bending a free-kick from 25 yards that seemed destined for the bottom corner, but Musa Dibaga reacted superbly, producing a fingertip save at full stretch to claw it away and preserve the Crues’ lead.
With four minutes remaining, Brooks wrapped up the points with a clinical finish at the back post from a Crusaders corner for his fifth league goal of the season.
Deep into stoppage time, Casey pulled a goal back with a close-range header from Michael Glynn’s corner, but it proved too little, too late for Jim Magilton’s men.
