Election Commission sources said that TMC candidate Minati Mishra won the Bankura seat by a margin of 15,139 votes defeating her nearest CPI-M rival Nilanjan Dasgupta.
She bagged 72,954 votes while Dasgupta polled 57,815 votes. Bharatiya Janata Party candidate Manisha Dey Chatterjee secured 7,910 votes.
Kashinath Mishra, whose death caused the by-election in Bankura, had won the seat by a margin of 29,080 votes in the 2011 assembly poll.
TMC candidate Mamata Bhuniya defeated Samar Mukherjee of the CPI-M in Daspur, West Midnapur district, by 18,919 votes.
The TMC candidate polled 94,860 votes and his CPI-M rival bagged 75,941 votes.
The by-election in Daspur was necessitated by the death of sitting TMC legislator Ajit Bhuniya.
Bhuniya had won the Daspur seat by a margin of about 25,000 votes in last year's assembly poll.
The Congress, however, did not put up any candidate in any of the two seats.
The TMC victory came on the heels of its recent civic election success which saw the ruling party winning four of the six municipalities.
Asked to comment on the reduced winning margin in both the seats compared to the 2011 assembly elections, TMC all-India general secretary Mukul Roy said that percentage of votes cast in by-elections are normally less than the full-fledged assembly elections.
Roy said that in the Bankura by-election, 67 per cent voting was registered as against 87 per cent in the 2011 assembly election, while in Daspur 73 per cent votes were cast as against 81 per cent earlier.
"Our party had won the Bankura by-election by bagging 49.42 per cent votes compared to 54 per cent votes in last year's assembly election. We consider the result as good even though there was a 20 per cent drop in the voting percentage this time," Roy said.
The by-elections to the two seats were held on June 12.