Japan had qualified in first place but were forced to settle for silver, with a Joe Fraser-inspired Britain surging from the foot of the standings at the halfway stage to earn a remarkable bronze at Italy's expense.
All three medalling nations have secured a place at the Paris 2024 Olympics.
China's winning team boasts 2021 world all-around champion Zhang Boheng, Tokyo 2020 Olympic parallel bars gold medallist Zou Jingyuan, Sun Wei, You Hao and Yang Jiaxing.
"We did so much better compared to the qualification," said Zhang. "After one day of refreshing our minds and reflecting after the qualifiers, we got great momentum and rhythm today.
"On the first rotation we kind of struggled a little bit with nerves, especially on pommel horse, which is difficult to control somehow."
China, who were fourth in Monday's qualifying competition, won gold with a total of 257.858 to take home a record-extending 13th gold in the event.
Japan held on to take silver on 253.395 while host nation Britain finished on 247.229, ahead of the Italians on 245.995.
On Tuesday the United States won the women's team competition for an unprecedented sixth time in a row.
They were pushed all the way by Britain, roared on by a vociferous home crowd, but eventually clinched gold by more than three marks.
The absence of Simone Biles and Olympic all-around champion Sunisa Lee raised doubts about whether the US could cling on to their crown but Jordan Chiles, Leanne Wong, Jade Carey, Shilese Jones and Skye Blakely produced an emphatic response.
