The event means that Zuma will continue as the ruling African National Congress (ANC) President and that of the country.
Asked what he believed the chances were of Speaker Baleka Mbete allowing the vote to take place by secret ballot again, he said he did not see this as crucial.
UPDATE: President Zuma has survived yet another motion of no confidence with 198 MPs supporting him and 177 against. Both Zuma and the Guptas have dismissed the accusations.
Opposition parties have planned a march in the streets of Cape Town where parliament is located to push for Mr Zuma's removal.
Maimane added that South Africa's current problems, including an economic recession and the extent of corruption allegations against Zuma, ministers and key institutions, constituted extraordinary circumstances that justified early elections.
A 201-vote majority would be needed to remove him from power, and the ANC holds 249 seats in the 400-seat parliament.
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More than two-thirds of voters, or 68%, say transgender people should be able to serve in the military, according to the poll. The data marked the lowest approval rating that the polling group had recorded for the president since he assumed office.
The party, which has ruled South Africa since the end of apartheid in 1994, is deeply divided and several ANC lawmakers have voiced criticism of the 75-year-old Mr Zuma.
Inside parliament before the vote, the ruling ANC had held a last-minute meeting behind closed doors to try and ensure its legislators' support for the motion.
After the result, Mr Zuma went outside parliament to thank his supporters.
Zuma is due to step down as head of the ANC in December, ahead of the 2019 general election. This time, at least 26 ANC MPs voted for his departure.
"We do not nor have we ever doubted their loyalty and discipline in relation to the decisions of the movement", the ANC said. Against this background, the Rand seems destined to weaken further, particularly if worries over the central bank's independence grow and/or Moody's decides to follow its rivals by downgrading the country's credit rating to junk. He also has been accused of mismanaging the economy.
The party said it will never surrender the country to Zuma's friends, the Gupta family.
"Section 50 of our Constitution states that the President must dissolve the National Assembly if the Assembly has adopted a resolution to dissolve with a supporting vote of a majority of its members, and three years have passed since the Assembly was elected", he said.