The home side were looking to build on a positive performance last time out, despite suffering defeat away from home against Southampton.
There were little to no chances in the opening moments of the game as both sides looked to settle into possession and establish control.
A good team move almost created the opener as Nwosu found Jai Bansoodeb, who carried the ball towards the edge of the box before firing narrowly over.
The young Bees were first to strike, with Nwosu peeling away from his marker before steering a close-range finish past the goalkeeper following a cross from Coran Madden.
The away side could have levelled as Reece Bastafield fired a free-kick towards goal from 25 yards, but Layton Nicholls stretched to tip the ball onto the post.
Danyal Iqbal went on a good run in the box and Nicholls was again positioned well to make the save with his right boot.
Nwosu could have scored his second of the game on 65 minutes as he was played in on goal but William Rutter did well to smother the striker and the ball in one motion.
The second came on 85 minutes and it was centre-back Harry Biggs who sealed the win as he found the net from a corner.
There was enough time for a third as Nwosu found Trialist A in the box who had the easy job of sliding the ball into the net.
Brentford turned on the style late on to secure their first three points of the season in the U18 Premier League.
McDermott's side are next in action on Tuesday 26 August as they begin their U18 Premier League Cup campaign with an away trip to Burnley.
Brentford: Nicholls, Fanoiki, Foster-Jones (Biggs 64), Oladapo-Gamu, Danso, Cohalan, Madden (Trialist A 81), Noni (Roca 64), Nwosu, Bansoodeb, Kasujja (Mason 89)
Subs not used: Lyon, Serme, Balogun
Booked: Madden 23
West Brom: Rutter, Lartey, Round (Saeed 87), Sankoh (Williams 76) , Perkins, Saa (Hutchinson 46), Colgan (Shaw 46), Iqbal, Camara (Nasibu 87), Bastafield, Billings
Subs not used: McDonald,
Booked: Hutchinson 56, Perkins 79