Polls opened at 0400 GMT in the cliffhanger vote pitting Tsipras's radical left Syriza party against the conservative New Democracy bloc headed by tough-talking ex-lawyer and defence minister Vangelis Meimarakis, who has wiped out the gap between right and left during the election campaign.
Over 9.8 million Greeks were registered to vote in an election that will select a new government to implement a three-year bailout adopted by the country's parliament last month. The divisive decision led to the toppling of Tsipras's government.
Many voters said they were casting their ballots with a heavy heart, knowing that whichever party wins, they will still be facing the tough reforms Tsipras agreed in July in return for a new 86-billion-euro (USD 97-billion) international rescue.
"I'm voting with great sadness," said Nikos, a former engineer.
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"My two children are unemployed and are living on my pension, which has been cut from 1,200 euros ($1,350) to 750 euros," he told Skai TV.
"Whoever is elected the result will be the same," added Yiannis, also a pensioner.
"Greece has been owing money for its entire existence, and as long as this happens it will suffer."
Ballots close at 1600 GMT, at which point exit polls will be available. The interior ministry is expected to make an announcement on the first official results after 1800 GMT.
Tsipras, a charismatic former student leader, was elected in January with 36.34 per cent of the vote, becoming Greece's youngest prime minister in 150 years and a beacon for anti-austerity campaigners across the European Union.
But the latest figures now show Tsipras leading Meimarakis by a narrow margin, with polls putting the Syriza leader's advantage at between 0.7 and 3.0 per cent.