The presidency and Zuma's ruling African National Congress (ANC) have denied demanding landing permission for the flight carrying nearly 200 guests for a wedding.
But a diplomatic protocol chief Bruce Koloane said he acted "under pressure from No. 1", a direct reference to Zuma, the report said.
Koloane has been suspended and not spoken on the matter. The government report said he used deception to obtain military landing permission.
Opposition members of parliament charged that the Gupta family at the centre of the affair and whose companies have employed two of Zuma's children in high profile roles, was wielding undo influence over Africa's largest economy.
"There is a widely held perception that when the Guptas say 'jump', the president says, 'how high?'," David Maynier, an MP with the opposition Democratic Alliance, said in parliament.
The Gupta brothers Atul, Ajay and Rajesh have a business empire that stretches from mining to media. They have been major financial backers of both Zuma and the ANC.
The scandal has ranged from farce - border officials had to interrupt the four-day wedding at the luxurious Sun City resort to have guests fill in belated customs forms - to a potentially serious diplomatic incident.
The report also implicated officials from the Indian High Commission to South Africa in the deception, charges which the embassy denies.
The report also found lounges at the air force base had been decorated to welcome the visitors who were entertained by singers and dancers. They were then taken in a convoy of luxury cars to the resort - under police escort.