Around 150 people have been killed since the opposition launched a campaign against the election in October while more than a thousand opposition leaders and activists have been detained in a crackdown denounced by rights groups.
A huge security operation involving 50,000 troops has been mounted to ensure the eight hours of voting passes off smoothly once polling stations open at 8:00am (0200 GMT).
But after scores of arson attacks on polling stations and with the opposition trying to enforce a general strike, officials admit turnout could be even worse than the previous low of 26 percent in a rigged 1996 election.
Hundreds of buses and other vehicles have been firebombed in recent weeks, and the fear factor is expected to further deflate the turnout.
The main opposition Bangladesh Nationalist Party (BNP), whose leader Khaleda Zia has been confined to her home, decided to boycott the poll after Hasina refused to stand aside and let it be organised by a neutral caretaker government.
With the opposition charging that the election lacks all credibility, analysts warn it will likely fuel violence in a country that has already seen its bloodiest year of political unrest since Bangladesh broke free from Pakistan in 1971.
The former East Pakistan is the world's eighth most populous nation but also one of the poorest in Asia and more turmoil will undermine efforts to improve the lot of its 154 million population. A third of them live below the poverty line.
Hasina, who beat two-time premier Zia in a December 2008 election, has accused her bitter rival of snubbing attempts to reach a consensus on the electoral framework.
"She spurned my offer for dialogue and instead choose the path of confrontation," Hasina said in her final pre-election address. "She held the country hostage in the name of strikes and blockades."
Zia in turn says the polls cannot be fair as long as they are overseen by Hasina, calling what is effectively a one-party contest a "scandalous farce".
Both women, who have a notoriously poisonous relationship, blame each others' supporters for the violence which has capped a year of political unrest.
A local rights group says more than 500 people have been killed since January 2013, a toll that includes victims of clashes between the security forces and Islamists angered by the conviction of some of their leaders for war crimes dating back to the 1971 conflict.
The main Islamist party, Jamaat-e-Islami, has been banned by the courts from taking part in the election and its leaders are either in detention or have gone into hiding.
Alarmed by the violence as well as being "disappointed" by the BNP's boycott, the United States has declined to send observers as have the European Union and Commonwealth.
The result is not in doubt as 153 of the 300 parliamentary seats are not being contested, giving a free run to Awami League members or their allies.
In total, 21 opposition parties have refused to take part in what is the 10th election in Bangladesh's troubled post-independence history.
It has already endured nearly 20 coups since 1975 and Hasina's powerful son Sajeeb Wajad evoked the spectre of another coup in a Facebook post this week when he railed against a "third force" of intellectuals.
Zia's party says Hasina is in danger of turning the country into an international pariah on a level with the likes of Somalia and Robert Mugabe's Zimbabwe.
A prolonged post-election crisis is expected to dampen growth rates which had averaged around six percent in the last five years.
The $22 billion garment industry, which accounts for 80 percent of the country's exports, is still reeling from the aftermath of the collapse of a factory complex last April which killed at least 1,135 workers and sparked lengthy industrial disputes over safety levels and rates of pay.