Four members in the 243-member house could not vote, reducing the total strength of the house during the trust vote to 239.
With the effective strength of the House reduced to 239 during voting, Bihar's new government needed 120 votes to win the confidence vote.
While Raj Bhallav Yadav of the RJD could not attend as he is in jail, BJP's Anand Shankar Pandey was absent as he is undergoing medical treatment outside the state. Congress' Sudarshan could not vote due to technical reasons as he was out of the House when the doors were shut for lobby division.
Chief Minister Nitish Kumar and Deputy Chief Minister Sushil Kumar Modi did not take part in the voting as both are members of the Legislative Council. However, they were present in the house.
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In the voting under lobby division, members in favour of the confidence vote went inside one lobby where they signed a register; those against it headed for another lobby and signed a register.
At the end, the speaker announced the result of the trust vote, with 131 in favour of the NDA and 108 against it.
The 131 votes in favour of Nitish Kumar comprised JD(U) 70, BJP 52, HAM 1, RLSP 2, LJP 2 and Independent 4.
The speaker's effort to decide the fate of the confidence motion through voice vote failed twice following shouting from both the treasury and the opposition benches.
Senior RJD MLA Abdul Bari Siddiqui demanded secret voting but was rejected by the speaker.
At the end of the confidence vote, the speaker announced its adjournment for an indefinite period.
The Bihar Assembly held a one-day special session today for taking up the trust vote by the JD(U) and NDA coalition government.
Speeches of senior leaders of various parties on the confidence motion moved by the chief minister were frequently disrupted by members of rival parties.
Modi spoke on behalf of the BJP while the chief minister spoke last.
Kumar, 66, was sworn in yesterday, returning to the National Democratic Alliance after four years. The day earlier, he had resigned as chief minister, breaking ranks with his allies -- Lalu Yadav's RJD party and the Congress.