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Buatsi, 23, won by knockout against Uzbek Elshod Rasulov - his second consecutive stoppage in Rio. He faces Abdelhafid Benchabla of Algeria next.
"I wasn't expecting to knock him out." Buatsi said.
Fellow Briton Pat McCormack progressed in the light-welterweight category, but Josh Kelly was eliminated from the welterweight category.
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Birtley boxer McCormack won his preliminary bout in the men's light-welterweight by split decision against Kazakhstan's Ablaikhan Zhussupov at Riocentro Pavilion 6.
McCormack was awarded both of the opening two rounds, eventually winning two rounds to one in the eyes of the judges.
"When they said split, my heart dropped a bit," McCormack said. "I was thinking they can't have given it to him.
"I thought I won very well but it is what it is - as long as I got the win. That's all that I've come for."
He faces the tournament number two seed - Yasniel Toledo of Cuba - in the last 16.
However Josh Kelly's Olympic Games are over after he was soundly beaten by unanimous decision by top-ranked Daniyar Yeleussinov, of Kazakhstan, in the welterweight division last 16 by unanimous decision.
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There are no British fighters in action in Rio on Friday, but Joe Joyce begins his Olympic super-heavyweight campaign against Cape Verde's Davilson dos Santos Morais at 23:00 BST on Saturday.
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British boxer Joshua Buatsi has reached the quarter-finals of the men's Olympic light-heavyweight competition.