The Tottenham Hotspur loanee replaced Mark Harris with 64 minutes on the clock, and the score at 1-0 to the Baggies.
Two minutes into stoppage time, a long Will Vaulks throw-in was flicked on by Elliott Moore into the direction of Scarlett, who guided a header beyond Alex Palmer in the Albion goal.
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Scarlett said: “I’m happy and I’m buzzing for the boys to get the result in the end, and for me, it was good to get that chance.
“I just had to anticipate it in the last minutes of the game. As a striker, you need to be ready for those kinds of moments, and thankfully it fell to me.
“It was a dream and a really good feeling, and hopefully there’s more to come now.
“I just have to be patient. My chances will come, and today it came, and I took it, so we’ll see what happens.
“It’s a challenge, but I’m up for the challenge. I’m ready to take it now. I’ve had a few loans now, but now it’s time to push on.”
During the international break, Scarlett was promoted from England’s Elite League squad, formerly the Under-20s, to the Under-21s for Euro qualifiers against Ukraine and Azerbaijan.
Scarlett was unused in a 2-1 win against Ukraine, but got a goal and an assist from the bench in a 7-0 romp over Azerbaijan.
The striker, who has previously captained the Elite League side, said of his impact against Azerbaijan: “That boosted my confidence. I needed that. Hopefully from now on, it’s positive.
“One of the best feelings in football is leading your nation out, I would say. That’s really good, and it helps when I come back to senior men’s football.
“I can be involved and let them know that I’m a leader too even though I’m young.
“I go and play football, and enjoy football. When I’m on the pitch, I’m the happiest I will be.”