It was the first time Jamie Milligan's side had hosted a competitive league game at the Sir Tom Finney Stadium in almost 10 months - and almost two years since Brig had taken on Hyde United.
The night got off to the perfect start for Brig, who took the lead within the opening six minutes.
Rob Apter saw his curling effort well saved by Joe Green, before Sinclair was first to the rebound to fire in for his first goal of the season.
Hyde then thought they had levelled on 20 minutes when Tom Morris headed in, but the linesman's flag was already up for offside.
Down the other end, Brig would shortly have their second of the evening. Ewan Bange was brought down inside the penalty area, before stepping up to take the resulting spot kick and calmly placing it down the middle.
Apter then almost made it three on the stroke of half time when his curling effort went just past the post via the aid of a deflection.
But Milligan's side wouldn't have to wait too much longer to extend their advantage. From the following corner, Matthew Flynn rose highest to power home a header - his first goal in a Brig shirt.
The hosts therefore went into the break with a 3-0 lead, and almost made it four on 54 minutes when Mark Yeates's accurate free kick from 25 yards drew an excellent diving save from Green.
It was the visitors, however, that would score the fourth goal on 60 minutes. A low cross from the left side of the penalty area found Liam Hardy, who tapped it over the line to reduce the deficit.
Brig's advantage would be restored five minutes later, via their second penalty of the evening.
Sinclair was brought down by the goalkeeper, before stepping up himself and converting the spot kick for his second goal of the evening.
Brig twice went close in the final stages, with Apter seeing his efforts go narrowly over the bar on both occasions. The full-time whistle then blew, with the 4-1 win representing an excellent evening at the office for Jamie Milligan and his side.