During the division of votes, the government got 142 votes against 51 in favour of the motion in the 294-member house.
The motion moved by Leader of the Opposition Surya Kanta Mishra and five other Left Front legislators read "This House express its want of confidence in the council of ministers".
The debate over the motion was held in the absence of the chief minister who was away in Delhi.
An SUCI(C) member Tarun Naskar participated in the debate and voting.
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This was for the first time a no-trust motion was brought against the TMC government since it came to power in May, 2011.
The speakers against the motion, including finance minister Amit Mitra, education minister Partha Chatterjee, urban development minister Firhad Hakim and panchayat minister Subrata Mukherjee, highlighted the government's performance in revenue earnings, agriculture and housing among others and the success in the restoration of peace in the former Maoist stronghold of Jangalmahal.