Josh Batty needed treatment after a poor challenge from Robbie Start in the opening stages, but Brigg soon settled down and took the lead through Conner Harman, who was played in by Stephen McCarron before rounding Ben Voase to net the opener.
A few minutes later Harman turned provider delivering a long ball over the top for Batty to slot in the second goal.
Beverley halved the deficit when Alex Knaggs bundled in the rebound after Matty Plumber’s header from Matty Stafford’s corner rattled the crossbar.
Soon afterwards Olly Baldwin equalized finding the bottom corner with a free kick from about 25 yards.
Brigg retook the lead on the stroke of half time through Owen Vincent – he latched onto James Petronzio’s cross and fired home sending the Zebras in 3-2 up at the break.
The second half began with Harry Griffin and Joe Pugh coming close at either end.
James Piercy then headed just wide from Plumber’s free kick before Baldwin’s effort was well blocked by Petronzio.
Baldwin had looked dangerous and minutes later he was narrowly off target with a powerful strike from the edge of the box.
At the other end, Voase pulled off a great save to deny Vincent at full stretch.
Afterwards, Dayle Hutson was unlucky not to win a penalty after being brought down by Eric Onyaka in the area. However, seconds later Alfie Usher ran onto McCarron’s delightful pass and kept his composure to double Brigg’s advantage.
The hosts responded with Baldwin fizzing in a low cross for Joe McFadyen to pull one back.
In stoppage time Vincent’s 20-yarder made the final score 5-3 to the Zebras.
This was Brigg’s highest scoring and most entertaining match of the season.