Belyavskiy suffered a heartbreaking end to his competition when he fell on his last routine, the horizontal bar, to drop out of contention for the gold medal and miss out on the podium completely.
"I only thought of doing the exercise from A to Z without any thoughts, without falls, but it happened," Belyavskiy told reporters.
"Maybe I'm just lacking some luck. I have three more finals, so I'm going to concentrate on them."
The medals were a much-needed boost for China as the country looks to recover after a disappointing showing in the men's competition at the 2016 Rio Olympics, where they took a lone bronze in the team event. Cuba's Manrique Larduet finished fifth, while Briton NileWilson was sixth and Yul Moldauer of the United States came seventh.
Ukraine's Oleg Verniaiev was considered favourite for gold prior to the event but his hopes were dashed when he fell off both the pommel horse and horizontal bar. He finished in eighth.
The women's all-around final takes place on Friday.
(Writing by Jahmal Corner in Los Angeles)
