The pressure was beginning to show for both sides and the game changed when Bears' Joel James and Cougars' Liam Darville were sent to the sin-bin.
The resulting penalty went to the away side and they scored a crucial try through Ash Lindsay.
The game was finally put to bed moments later when Paul White crossed before Hamish Barnes rounded off the scoring for the Cougars.
Brook converted two of the three late tries to add a gloss to the final scoreline but it was a performance the Bears could be proud of on a ground-breaking day for the sport in Coventry.
Bears: O'Mara, Warrilow, Medforth, Reid, Bass, Redman, James, Beddows, Lobwein, Morrison, Thompson, Barratt, Hughes Replacements: Geurtjens, Beecham, Miliszewski, O'Sullivan.
Keighley: White, Gabriel, Sheriffe, Barnes, Finigan, Darville, Brook, Cheerryholme, Feather, Rawlins, Hawkyard, Martain, Lindsay Replacements: Ollett, Lynam, Peltier, Bailey.
Referee: John McMullen