With more than a quarter of the votes counted, the leftwing Syriza party had a larger-than-expected lead of 35 percent against 28 percent for the conservatives.
This led the leader of the conservative New Democracy party, Vangelis Meimarakis, to admit defeat.
"It appears that Mr Tsipras' Syriza is first, I congratulate him," he said.
At Syriza party headquarters, the boyish Tsipras was greeted with a huge round of applause by supporters who clapped and shouted when the results of the exit polls were announced, breaking into Italy's revolutionary anthem, Bandiera Rossa, Italian for "Red Flag".
Wearing his trademark open shirt and cheery smile, he said after casting his ballot that voters will elect "a fighting government" ready for the "confrontations necessary to move forward with reforms".
Hands-down winner of a January general election, then with 36.34 per cent of the vote, Tsipras resigned in August and called snap elections, gambling crisis-weary Greeks would give him a new mandate despite his controversial austerity deal with European leaders.
After winning office on an anti-austerity ticket, he agreed in July to more punishing austerity for the nation in exchange for its third financial rescue in five years.
But the move alienated many Syriza supporters and split the party, with a fifth of its anti-euro hardline MPs walking out, forcing Tsipras to call the election.
He went to the polls facing a strong challenge from the conservative New Democracy party led by ex-defence minister Meimarakis, who slammed the former leftwing premier for his U-turn with the country's creditors and for his seven chaotic months in power.
Casting his vote, 61-year-old Meimarakis said: "Voters want to send away...The lies, the misery, the posers and bring truth and real people."
The reforms were agreed in return for a new 86-billion-euro (USD 97-billion) international rescue, Greece's third in five years.
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