The Zebras made a promising start with Josh Batty heading wide of the top angle of the goal before firing past the upright.
Alfie Usher’s effort was then cleared off the goal line and Stephen McCarron struck a fierce drive over as Brigg continued to threaten.
Minutes later Conner Harman raced clear and was thwarted by a great save from Henry Kendrick, who did brilliantly to save his close-range shot with an outstretched leg.
Afterwards Wakefield improved with Billy Mole coming close after running onto Robbie Miller’s ball over the top.
A quick-fire double towards the end of the half saw Wakefield lead 2-0 at the interval.
In the 42nd minute Jody Barford tipped over Cory Woodward’s free kick at full stretch. However, the resulting corner led to Mason Rubie scoring the opener.
Less than 3 minutes later Kieron Ceesay was brought down in the area for a penalty to Wakefield. Billy Mole converted from the spot to give the visitors a two-goal advantage.
Brigg came out with all guns blazing in the second half almost pulling one back through Alfie Usher, whose shot struck the outside of the post.
On 59 minutes Wakefield added a third when Lewis Stephens blasted home the rebound once Barford kept out his first attempt.
Brigg nearly pulled one back within two minutes, Martin Pembleton’s free kick coming back off the post after Jack Richardson was fouled just outside the box.
Richardson then won a penalty going down under Haydn Ward’s challenge, but Batty’s spot kick was well saved by Kendrick.
Brigg kept going late on with Pembleton having a powerful strike blocked inside a crowded box, but there was no consolation goal.
The Zebras were very unlucky not to find the net being denied by the woodwork twice and Kendrick many times in a Man-of-the-Match display.
The next few matches will all be against tough opposition as Brigg go in search of points to move higher up the league table.