The game was scrappy after a six-week lay-off, but it was the result that mattered most.
Paul Wiper opened the scoring and as Slazenger grew in confidence Simon Chamberlain converted coolly with a penalty flick after a Brigg defender had stopped the ball on the goalline with his foot.
Brigg rallied and forced a goal, but Slazenger restored their two-goal cushion when Phil Midgley took advantage of the 'self-pass' rule to drive into the D and fire home.
Brigg pressed higher up the pitch where they were caught on the break by Slazenger. And Dan Perry tucked away the killer fourth goal.
Slazenger have a tough fixture at Leeds University on Saturday but go there aiming to cause an upset.