Zou overcame Barnes 15-0 in the last-four stage at the Beijing 2008 Games and he claimed another win, this time on countback after the judges scored the bout level at 15-15.
Barnes' fellow Irishman John Joe Nevin was in action moments later in the Bantam Weight division and scored a stunning victory over top seed and reigning world champion Estrada Alvarez of Cuba.
Alvarez looked to take advantage of his longer reach in the opening stages but Nevin was up for the challenge and found a way through, notably with a big right hand that rocked his opponent's head back.
He took the opener by two points and then edged round two 7-6 despite Alvarez seemingly getting back into the contest with some well-directed shots.
Nevin held his nerve to wrap up a 19-14 success, and will face Great Britain's Luke Campbell in the final.
Campbell eased past Japan's Satoshi Shimizu 20-11.