The fifth stage of the bill passed by 81 votes to 76 and now goes to the upper house, the Seanad, for approval.
Once the legislation is through, parliament is expected to be dissolved and a general election called.
The governing coalition led by Fianna Fail lost its majority last week.
Finance Minister Brian Lenihan brokered a deal on Monday with opposition parties to fast-track the finance bill and then call general elections earlier than planned.
The government also needed the support of several independent Dail members to get the bill passed in its various stages.
The finance bill is Ireland’s final legislative commitment under the 85bn euro ($113bn; £72bn) EU/IMF rescue plan.
Among other things, it will raise income taxes and close tax-dodging loopholes.
The upper house will meet on Friday and Saturday to approve the bill and the Dail may meet again on Saturday evening if any further amendments need to be debated.
Prime Minister, or Taoiseach, Brian Cowen would then ask the president to dissolve the government, which reports suggest could happen any time between Saturday and next Tuesday.
There is widespread speculation that the elections will be on 25 February.
Mr Cowen will not be contesting the elections – he stepped down as Fianna Fail leader and his former foreign minister Micheal Martin was elected to succeed him.
Analysts expect Fianna Fail to suffer a crushing defeat at the polls, as voters blame them for mismanaging the economy.
The main opposition parties have said they want to re-negotiate parts of the bail-out package, particularly the interest rate on loans.
But the European Central Bank stressed on Thursday that any future government in Dublin would have to abide by the deal.
“It doesn’t happen that when you have a change of government that the next government reneges on commitments,” ECB Executive Board member Bini Smaghi told Ireland’s RTE channel. – Bbcnews