The midfielder teed up Danny Welbeck for his winner as Liverpool were beaten 2-1.
It was a fourth win in five games for the Seagulls, who have started just 12 different players in those games.
The settled side in which Fabian Hurzeler has put his faith means players such as Georginio Rutter, Yasin Ayari, Carlos Baleba and now Kaoru Mitoma are all pushing for starts.
Hinshelwood said: “There's massive competition and it's about getting your chance and holding on to your shirt.
“I've been lucky to do that the last few games. I'm working hard every day in training and in games to keep hold of my shirt.
“I think the more competition, the better for the team.
“If everyone is fighting every day for their shirt, then that only brings a healthy working environment.”
Hinshelwood scored the winner at home to Liverpool late last season but had to wait for a lengthy VAR check to confirm Matt O’Riley was onside.
This time the check was on Welbeck as Hinshelwood played the ball back across to him.
Hinshelwood said: “As soon as the ball was spread to Minteh, I know what he likes to do.
“He likes to go on his left and put early crosses in, so I was able to start my move early.
“I obviously got ahead of (Virgil) van Dijk, I think it was, and saw Welbs was alongside me.
“I obviously squared it to him and it was a good finish.
“Thankfully, it was onside. I was a bit worried because when I passed it to him, I thought it was slightly ahead.
“But no, it was a massive relief when it went in and it was a massive goal in getting the 2-1 win.”