Early results showed Hasina racing into a clear lead, winning each of the first 29 seats declared – some by tens of thousands of votes – according to Channel 24, which is compiling results from around the country.
The deadly violence and bitter rivalry that marred the election campaign spilled over into voting day, even as authorities imposed tight security with 600,000 troops, police and other security forces deployed across the country.
Ten people were killed in clashes between Hasina's ruling Awami League party and supporters of the main opposition Bangladesh Nationalist Party, police said, while three men were shot by police who said they were protecting polling booths.
An auxiliary police member was also killed by armed opposition activists, according to officials.
Hasina, 71, has been lauded for boosting economic growth in the poor South Asian nation during her decade in power and for welcoming Rohingya refugees fleeing a military crackdown in neighbouring Myanmar.
But critics accuse her of authoritarianism and crippling the opposition – including arch-rival Khaleda Zia who is serving 17 years in prison on graft charges – to cling on to power.
The BNP-led opposition alliance Sunday accused Hasina's party of using stuffed ballot boxes and other illegal means to fix the result, which was to be announced Monday.
BNP spokesman Syed Moazzem Hossain Alal told reporters there were "irregularities" in 221 of the 300 seats contested. Its Islamist ally Jamaat-e-Islami said it would reject the results.
"Voters are not allowed to enter booths. Especially women voters are being forced to vote for the boat," Alal said, referring to the Awami League symbol.
'We'll cast your vote'
Bangladesh election commission spokesman S.M. Asaduzzaman told AFP the body had "received a few allegations of irregularities" and was investigating.
Authorities ordered mobile operators to shut down high speed internet services until midnight Sunday "to prevent the spread of rumours" that could trigger unrest.
Voting in the capital Dhaka was largely peaceful as convoys of soldiers and paramilitary forces were on the streets where most traffic was banned.
However voters in provincial areas reported intimidation. Atiar Rahman said he was beaten by ruling party activists in the central district of Narayanganj.
"They told me not to bother, 'We'll cast your vote on your behalf'," he told AFP.
The opposition said the unrest was stirred up to deter voters, and presiding officers reported a low turnout across the country.
Sunday's deaths brought to 18 the official police toll for election violence since the ballot was announced on November 8.
Police said they acted "in self-defence" in the southern town of Bashkhali, when they fired on opposition supporters who stormed a polling booth, killing one.
In a separate incident a man was shot by police after he tried to steal a ballot box.