President Xi Jinping has spent the past three years waging war on deep-seated corruption, saying it threatens the very survival of the ruling Communist Party.
Scores of senior officials in the party, the government, the military and state-owned enterprises have been brought down, including Zhou, jailed for life in June after a secret trial in China's most sensational graft scandal in 70 years.
A court in Hanjiang in the central province of Hubei jailed Jiang Jiemin, the former head of state-owned China National Petroleum Corporation (CNPC), the country's top energy group, for 16 years for bribery and abuse of power.
Another court in a different part of Hubei called Xianning sentenced Li Chuncheng, who was a deputy Communist Party boss in the southwestern province of Sichuan, to 13 years in jail on the same charges.
The announcements came on the courts' official microblogs.
Jiang was a close associate of Zhou, the once-powerful domestic security chief and a former member of the elite Politburo Standing Committee, the most senior person to have been charged with corruption in Xi's anti-graft campaign.
Zhou had also been at CNPC, the parent company of PetroChina Co. Ltd., having risen through the ranks to serve as general manager from 1996 to 1998.
State television showed pictures of a grim-faced Jiang, who also ran the state asset regulator for five months before being sacked in September 2013, sitting in the dock with a policeman at each side.
Jiang took more than 14 million yuan ($2.21 million) in bribes between 2004 and 2013, and with Zhou's connivance broke rules to provide assistance to others in their business dealings, the court said without elaborating.
Jiang admitted his guilt and provided evidence of his crimes and so received a more lenient sentence, the Hanjiang court said, adding he would not appeal.
He had served as CNPC chairman from 2011 to 2013 and had gone on trial in April. It is not clear why the verdict took so long to come out.
The former senior Sichuan official Li took 19.8 million yuan in bribes, but also got a lighter sentence for his confession and cooperation, the court said.
While the statement did not use Zhou's name, Li was mentioned in Zhou's trial as someone who used his influence to help others' illegal business activities. Li also went on trial in April.
Zhou was party boss of Sichuan from 1999-2002 and it became one of his powerbases.
($1 = 6.32 yuan)
(Reporting By Adam Rose, Ben Blanchard, Judy Hua and Megha Rajagopalan; Editing by Nick Macfie)