Zhou died last month at the age of 93 and was hailed in a party statement as being an "excellent" party member.
The Xinhua news service said Zhou's standing was illustrated by the ranks of the mourners who attended Monday's cremation at Babaoshan Cemetery.
Zhou, a former consultant to the Central Military Commission General Office, joined the Chinese Communist Party in 1938 and accompanied Deng to Juangxi Province in 1969.
Deng was one of the principals of China's Great Leap Forward plan and led China through the 1980s. He died in 1997.