The banks have been closed since June 29 to stanch a bank run, with Greeks limited to cash withdrawals of 60 euros ($67) per day, and the ECB had not raised the credit it makes available since last month. The extra credit is needed to make up for the constant outflow of money from the banks.
It remained unclear how quickly Greece's banks could reopen or when they might ease the limits on cash withdrawals.
The government must now pass a second bill through Parliament next week, which includes reforms to civil justice procedures.
The requirements are part of a deal reached between Prime Minister Alexis Tsipras and other eurozone leaders after a marathon summit in Brussels last weekend, under which Greece must implement harsh austerity measures, including tax hikes and pension cuts, in return for the start of talks on its third bailout.
Tsipras, who was elected in January on promises of repealing bailout-related austerity measures, has acknowledged the deal tramples on most of his election pledges, but insists he had no other option than to accept the harsh terms offered by lenders to ensure his country's financial system didn't collapse.
"We had a very specific choice: A deal we largely disagreed with, or a chaotic default," he told parliament ahead of the post-midnight vote.
Lawmakers voted 229-64 to implement the bill, in a vote that saw dozens of lawmakers from Tsipras' own radical left Syriza party dissent and vote against him. The bill passed with a massive majority thanks to the support of three pro-European opposition parties.
Thirty-eight party lawmakers defied Tsipras — nearly one-in-four — by voting against or abstaining. They included Tsipras' powerful energy minister, the speaker of parliament and Yanis Varoufakis, the former finance minister who headed Greece's bailout strategy until his replacement 10 days ago.
The government described the vote as marking a "serious division" among its lawmakers, and indicated that dissenters in Tsipras' Cabinet would be swiftly replaced in a reshuffle.
"Today, Parliament took the first important step for the deal, voting for the difficult measures," government spokesman Gabriel Sakellaridis said. "But the results of today's vote constitute a serious division in the unity of Syriza parliamentary group," he said. "The prime minister's and the government's priority is the successful conclusion of the agreement in the immediate future."
The Moody's credit ratings agency said the vote meant the country had dodged imminent danger, but that it still faced risks.
"The Greek parliamentary vote averts an immediate disorderly default and potential exit from the euro area, but risks remains elevated given Greece's weak institutions and substantial political scepticism on the bailout conditions," it said.
The four-week loan that European Commission President Juncker revealed Thursday would allow Greece to meet a debt repayment worth $4.6 billion to the ECB on Monday and to pay arrears of 2 billion euros to the IMF.