The government has agreed to incorporate a key amendment demanded by the opposition BJP, which allows searches or raids by the CBI or police on an officer accused of corruption without notice.
The proposed anti-graft law provides for a Lokpal or national ombudsman to investigate corruption charges against public functionaries.
Law Minister Kapil Sibal said all parties rose above politics to pass a Bill that the people wanted.
Anna Hazare said the Bill, if passed, could reduce corruption by half and help the common man get justice. "It is critical that the government's control on the CBI goes," said the Lokpal crusader.
Anna Hazare has written to Congress' Rahul Gandhi and BJP's Arun Jaitley thanking them for backing the Bill. He has disagreed vehemently with Arvind Kejriwal, his one-time protege, who has said the Lokpal Bill lacks teeth.
The government's floor managers on Tuesday persuaded the Samajwadi Party of Mulayam Singh Yadav to tone down their stance and allowed the party's Ram Gopal Yadav to voice his objection before staging a strategic walkout ahead of the debate.
Congress sources say Rahul Gandhi has taken charge of the party's Lokpal strategy, which many see as the party's attempt to credit him with championing the anti-corruption measure ahead of national polls due by May.
This morning, Mr Gandhi met with Parliamentary Affairs Minister Kamal Nath and minister in charge of the Prime Minister's office V Narayanasamy - to discuss strategy to ensure the Bill's passing in Parliament.
The Congress party's redoubled push for the Lokpal Bill is being seen in the context of its humiliating defeat in the Delhi elections. Arvind Kejriwal's Aam Aadmi Party or AAP made a stunning debut with its promise to fight corruption, decimating the Congress after three terms.
In December, 2011, the Bill was cleared by the Lok Sabha but was stalled in the Rajya Sabha. It was then sent to a parliamentary committee for review. The amended version will be introduced in the Rajya Sabha. That version must then be cleared by the Lok Sabha.