Dronfield settled down to enjoy more possession in the opening minutes winning corner kicks that were headed clear.
After a slow start Brigg began to create openings. Appeals for a penalty kick were dismissed by the referee after Josh Batty tried to turn sharply past his marker inside the area.
Jack Richardson, who was excellent throughout, had a goal disallowed. He was caught offside as he tried to time his penetrating run into the box.
Batty made another strong forward run, but goalkeeper Lewis Naylor was alert to gather the loose ball and then tipped another shot over the crossbar.
Dronfield continued to withstand the home team advances and responded with a snap shot from Callum Mawbey going wide of the target.
Brigg cleared a free kick played in from the left wing and set up a counter attack, which ended with a shot from Jack Richardson being tipped over the crossbar.
Martin Pembleton’s attempt at goal flew past the top angle of the woodwork and the first half closed with another strike from Richardson being deflected out of play for a corner.
The second half began with Stephen McCarron coming close after good build-up work on the left wing.
Play was end to end with both sides showing solidity in defending. However, the stalemate was broken when Dronfield worked the ball forward down the right wing and into the penalty area for Samuel Bebbington to find the far top corner of the net with an excellent strike from 15 yards out.
Richardson immediately went close with a shot just wide and Tom Collins had to be quick off his goal line to collect the ball from another right-wing attack.
Brigg introduced Alfie Usher and Dayle Hutson and were soon back on level terms when Usher crossed from the left wing before James Petronzio applied the finishing touch into the bottom corner of the net.
Both teams pushed for a winning goal late in the game, but strong defending snuffed out clear-cut chances leaving the two teams still unbeaten in the league to date.
There is no fixture for Saturday 13th August, but the team travels next Wednesday to face Worsbrough Bridge Athletic and follows this at home to Harrogate Railway Athletic on Saturday 20th.