The vote of confidence took place amid a walk out staged by the Opposition as cross voting happened when three Rashtriya Janata Dal MLAs also voted in support of Nitish Kumar.
The coalition government won the floor test with a 129 majority.
The Deputy Speaker of the Bihar Legislative Assembly Maheshwar Hazari asked the members of the House who were in favour of the motion to stand at their places.
"(A total of) 129 votes have been received in favour of the motion. There were zero votes against the motion. Thus, this House passes the trust vote," the Speaker said on Monday.
Three Rashtriya Janata Dal (RJD) MLAs -Chetan Anand, Neelam Devi, and Prahlad Yadav went and joined the National Democratic Alliance (NDA) in the State Assembly.
On three RJD MLAs moving to the NDA side, RJD leader Bhai Virendra said that the public will not make them MLAs again.
While addressing the Assembly, Nitish Kumar took a swipe at his former Mahagathbandhan ally Rashtriya
Janata Dal and said that the latter indulged in "corrupt practices" during its rule in the eastern state.
He also said that the current NDA government would initiate a probe into these practices.
Earlier, the Bihar assembly passed the no-confidence motion against Bihar Assembly Speaker and Rashtriya Janata Dal (RJD) leader Awadh Bihari Choudhary ahead of the floor test of the Nitish Kumar government to prove its majority.
During the no-confidence motion, 125 members voted in favour of the resolution brought by the ruling alliance and 112 against.
RJD MLAs Chetan Anand, Neelam Devi and Prahlad Yadav were seen sitting on the treasury benches in the Bihar Assembly causing a jolt to the Opposition.
Reacting to this, former Bihar Deputy Chief Minister and RJD leader Tejashwi Yadav said "MLAs should sit on their respective seats till the end of voting, otherwise voting will be considered invalid."
Nitish Kumar had reportedly gone into a sulk after not being named the convenor of INDIA, the Opposition bloc that took shape through his efforts. He resigned as chief minister on January 28, his second volte face in less than 18 months.
The JD(U) has 45 MLAs in the House of 243 while its partners, the BJP and the Hindustani Awam Morcha-Secular (HAM-S), have 79 and four legislators respectively. The NDA has the support of 128 MLAs and the majority mark in the state assembly is 122.