There were Congress celebrations when victory became clear, with dancing supporters cheering, clapping and letting off firecrackers in front of party leader Sonia Gandhi's house in Delhi.
Prime Minister Manmohan Singh thanked MPs for "such a convincing victory".
"This will send a message to the world at large... India is prepared to take its rightful place in the comity of nations," he told reporters.
The US welcomed the result and said it would work closely with the Indian government to have the deal ratified.
The BBC's Sanjoy Majumder in Delhi says the vote had looked too close to call.
But the government managed to scrape through with the support of smaller parties and independent members.
India faces a general election next year and many political parties have used the debate over the nuclear deal to stake out their positions ahead of the polls, our correspondent says.
The deal itself is now more dependent on whether it gets through the US Congress before elections in November, than on political opposition in India.
Two days of debate on the nuclear accord ended in uproar amid opposition allegations of vote buying.
Opposition Bharatiya Janata Party (BJP) members waved fistfuls of money in the air, alleging that they had been offered bribes to abstain.
Opposition MPs wave 30 million rupees allegedly paid to buy their votes
Mr Chatterjee adjourned proceedings for several hours. He called it a "very sad day" for the Indian parliament, adding: "Nobody will be spared if found guilty."
The prime minister has promised his party will co-operate in an inquiry into the claims.
With the left withdrawing support, the government could rely on only 226 members in the 543-seat parliament, and needed 46 more to be absolutely sure of a majority.
India's media was awash with reports of alleged defections and desertions among MPs ahead of the vote.
Under the accord, India, which has not signed the nuclear Non-Proliferation Treaty, would gain access to US civilian nuclear technology and fuel.
Mr Singh called the victory "impressive"
In return its civilian nuclear facilities would be opened to inspection. Nuclear weapons sites would remain off-limits.
The communists fear the accord could give the US too much influence over Indian foreign and nuclear policy.
The main opposition Hindu nationalist BJP fears that the deal could compromise India's ability to test nuclear weapons in the future.
India is under pressure from Washington to sign the accord before the US presidential election in November.
Last week, Indian officials met members of the International Atomic Energy Agency (IAEA), the world nuclear regulatory body, in Vienna to discuss plans to safeguard India's civilian nuclear facilities.
The IAEA's approval of the plan is a key condition for enacting the deal.
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