The start of the game was end-to-end, with both sides having early chances. Felix Goddard saved a half volley from Darius Osei in the third minute, before Paul Dawson then found the side netting with an effort from a tight angle.
It was Brig's number 10 that opened the scoring on 14 minutes. From a short corner, Dawson hit a first time effort into the bottom right corner from inside the area.
It was almost 2-0 shortly afterwards when Nathan Pond rose highest to meet a free kick, but he could direct his effort past Myles Boney in the South Shields goal.
The Brig defence was then called in action on 25 minutes after Shields captain Robert Briggs hit the post. The follow up effort was saved by Goddard, before another block led to the ball being cleared.
Goddard then made another fine save on 36 minutes, tipping Mackenzie Heaney's 25-yard effort over the bar.
The second half started in a similar way to the first half, with opportunities at either end. Brig's first opening once again came through Dawson, who received the ball after Luke Mariette's driving run before seeing his effort saved.
It was the visitors, however, that equalised on 64 minutes, substitute Dylan Mottley-Henry finding the back of the net following a cutback.
Brig were then brought down to 10 men when Nathan Pond's foul was deemed to be a red card offence.
But the hosts continued to push in an attempt to find a winner, and Mariette controlled a cross-field pass on 78 minutes before firing narrowly over.
Then, in stoppage time, Sinclair-Smith was tripped outside the area as he searched for a route to goal.
Brig's number 11 stepped up himself before producing a moment to remember, finding the top right corner with a superb 25-yard effort that raised the roof at the Sir Tom Finney Stadium.
Match reporter: Ryan Smart