The bill was passed with two amendments approved by the Select Committee of the house, and will now go back to the Lok Sabha for getting its approval again.
An amendment of CPI-M leader P Rajeeve to recommit the bill to the Select Committee was put to vote, but was defeated.
The Janata Dal-United (JD-U) walked out of the house before the voting with leader Sharad Yadav saying they did not want to be a part of the process.
Other parties, including the Trinamool Congress, AIADMK, Bahujan Samaj Party (BSP), Biju Janata Dal (BJD) and Samajwadi Party (SP), voted in favour of the bill, making it possible for the bill to pass through the upper house where the government is in a minority.
As the house took up a debate on the bill, Bhupendra Yadav of the BJP said the legislation will bring greater transparency in mining.
"This bill will bring transparency in functioning of mines, delays will be less and the share of states in the minerals will increase," he said.
Pawan Varma of the JD-U, opposing the bill, said: "A very fundamental demand that states should be consulted was not accepted. The new bill divests states of their authority. It needs legal consultation."
Tapan Kumar Sen of the Communist Party of India-Marxist (CPI-M) said: "There is no hurry as it is being shown. We have never opposed auctioning, but it is being shown we are against auction. It is taking away states' rights."
The Trinamool Congress supported the bill with party leader Derek O'Brien saying, "We have given some suggestions which have been incorporated and the glass of water is half full. Let us not be negative."
A. Navaneethakrishnan of the AIADMK and Rajaram of the BSP also supported the bill.
Rajaram said: "This bill should have been brought long back."
He, however, wondered if the bill would be able to check the mine mafia.
Congress leader Mani Shankar Aiyar said the bill can be ultra vires of the Constitution as it takes away the rights of the states.
"There was restriction of time on the Select Committee but there was no restriction on interaction with states," Aiyar said, adding that while mining secretaries from the states were in Delhi, they were not allowed to be examined by the committee.
"There was no consultation with states. If the committee could have consulted with states, this report would never be in this form. We are likely to pass a bill which may be ultra vires to Constitution," he said.
"We express our opposition to the manner in which this government is legislating through ordinances, hurting the states' rights...," Congress leader Anand Sharma said as Deputy Chairman PJ Kurien put the bill to vote.