The vote approved putting into practice the tax hikes, pay cuts, privatisations and public sector redundancies approved in principle on Wednesday.
It was a retreat from the "grave scenario of default", the EU said.
Public reaction has been very hostile, and the debate has been accompanied by strikes and violent protest.
After hours of discussing the measures, MPs started voting shortly after 1600 (1300 GMT); an hour later, PM George Papandreou had secured enough votes to push the bill through.
Meanwhile, German Finance Minister Wolfgang Schaeuble said German banks and insurers had agreed to participate in a plan to continue lending to Greece, following a similar decision by French lenders.
Mr Schaeuble said German institutions would contribute 3.2bn euros ($4.6bn, ?2.9bn) to the plan.
Calm returnsMr Papandreou's ruling Panhellenic Socialist Movement (Pasok) has a slim parliamentary majority, with 154 out of 300 deputies. Thursday's bill was passed by 155 votes to 136.
Continue reading the main story Debate starts at 0930 local time (0630 GMT)Vote itself not before 1400Roll-call vote with verbal response by MPsPossible additional votes on individual articlesGovernment has a majority of eight over all other partiesCabinet to meet after the voteSome Socialist MPs had said they would vote against individual clauses such as an increase in heating oil levy and a rise in the minimum tax threshold.Clashes continued on Syntagma (Constitution) Square outside parliament overnight, as police fired tear gas at stone-throwing youths.
Calm now appears to have returned and the BBC's Malcolm Brabant in Athens says the city's street-cleaning crews have come out in force removing debris from two days of battles in the square.
Police had restricted access to the city centre to prevent demonstrators from obstructing members of parliament heading to vote on the new law.
Some Athenians have accused the police of heavy-handed tactics, and newspapers have railed against what one called "an orgy of state terror", our correspondent says.
Some accused the police of over-using tear gas.
Scores of people were treated for injuries and severe breathing problems.
Government confidentGovernment officials said they were confident that those who supported them in Wednesday's vote, when the package was approved in principle by 155 votes to 138, would also vote for implementation, known as enabling legislation.
Continue reading the main storyAll that has happened is that a default has been avoided at a moment when Europe's banks are still vulnerable”End Quote
Gavin Hewitt BBC Europe editor Its measures include:The setting up of a privatisation agencyPreparation for privatisation of state-owned real estateTax increasesCurbs on public sector recruitmentSocial security regulationsThe opposition New Democracy party, which voted against the government on Wednesday, has said that it will support some elements of the bill involving privatisation and spending cuts.
"We will do what we can to support the government," said MP Nikos Dendias, a former justice minister, quoted by Reuters news agency. "We will vote for two chapters of the bill today."
Continue reading the main storyTotal Greek debt
Greece is about to get a second bail-out from the EU, aimed at helping pay its debts until 2014. It also has to agree more cuts as part of the deal.The economy
The Greek economy is in dire straits. Retail sales have fallen 18% since 2008 and manufacturing output has dropped 30% in the same period.Working population
Greeks retire on average at 61. Tax evasion is widespread. Until 2010, public sector workers received two months extra pay a year in bonuses. EU demands
To meet EU demands, Greece must sell 50bn euros-worth of public assets by 2014, equal to 20% of GDP. Public sector pay is being cut 15%.BACK {current} of {total} NEXT Finance Minister Evangelos Venizelos has offered some concessions on tax, one of the most contentious parts of the package.The vote will enable Greece to receive the latest tranche of a 110bn-euro (?98bn) loan in time instead of defaulting.
But analysts say the real challenge will come after the loan is secured, and there is concern about whether the austerity measures can be effectively implemented in the face of so much public hostility.
Wednesday's vote prompted a furious response from protesters in Athens.
Sporadic violent clashes were continuing in the capital in the early hours of Thursday between masked protesters - armed with sticks and stones - and riot police firing tear gas and stun grenades.
Despite the unrest, European Commission President Jose Manuel Barroso and European Council President Herman Van Rompuy welcomed the result as a "vote of national responsibility" paving the way for a second aid package.
Continue reading the main story June 29: Parliament approves new austerity package June 30: MPs vote on details of implementing packageJuly 3: EU will sign off latest bail-out payment to Greece - 12bn euros - if both votes are passedJuly 15: Without the 12bn euros, Greece will defaultThe package of tax rises and budget cuts - worth about 28bn euros over five years - had been championed by Greek Prime Minister George Papandreou.Had it been rejected, Greece could have run out of money within weeks. The EU and the International Monetary Fund have demanded that the measures are implemented before they extend further loans to Greece.
Greek unions are angry that the government's austerity programme will impose taxes on those earning the minimum wage, following months of other cuts that have seen unemployment rise to more than 16%.
Once passed, European officials will start to finalise the details of a second bail-out, worth an estimated 120bn euros, designed to help Greece pay its debts until the end of 2014.
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