The vote followed a stormy debate in which dozens of lawmakers on the left of the ruling Syriza party rebelled against Prime Minister Alexis Tsipras and opposed the package, which passed with the support of opposition parties.
The package passed with 229 votes in favour in the 300-seat chamber but 38 Syriza lawmakers abstained or voted against the government, including including former Finance Minister Yanis Varoufakis and the current Energy Minister Panagiotis Lafazanis, Deputy Labour Minister Dimitris Stratoulis and speaker of parliament Zoe Constantopoulou.
Listen: The BBC's Seref Isler speaks with SBS reporter Kristina Kukolja.
The result opens the way for talks on a third bailout to begin with European partners, but leaves the future of the leftist Tsipras government unclear following the split in his party ranks.
Outsiide parliament, clashes broke out at an anti-austerity rally by thousands of protesters.
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Riot police used pepper spray and tear gas on Wednesday night to fight back youths in the crowd who were hurling Molotov cocktails and rocks at police.
Police said about 12,500 people were at the rally at Syntagma Square.
Greek energy minister says would resign if PM asked
Greek Energy Minister Panagiotis Lafazanis said on Thursday he would quit if Prime Minister Alexis Tsipras sought his resignation, after he and party rebels downvoted a crucial reforms package approved by parliament to stave off bankruptcy.
Lafazanis was among 38 lawmakers of left-wing Syriza who rejected or abstained from a tax and fiscal reform bill required for the country to start bailout talks with foreign lenders.
"If at any point my resignation is sought it would be at the disposal of the (Prime Minister)," Lafazanis told journalists.
"We are lawmakers of this government, we support it wholeheartedly. We support Syriza in government and we support the Prime Minister. We don't support the bailout," he said, adding that he did not believe the situation warranted snap elections.