As a division was called for by some members during the Bill's passage, 147 members voted in favour and 42 against it.
The Lok Sabha has already passed the Bill, under which the government can designate individuals as terrorists if the person commits or participates in acts of terrorism, prepares for or promotes terror or is otherwise involved in terrorism.
Replying to the debate, Home Minister Amit Shah said earlier that it is important to name terrorists individually as it had been seen that when terrorist organisations were banned, the terrorists floated another outfit.
He also said that countries like the US, Israel, Pakistan and China designate individuals as terrorists.
Many opposition parties opposed the provision, saying this could be misused.
Congress leader P. Chidambaram said that tagging an organisation as a terrorist was different from branding an individual. He stressed that the provision violated individual liberty.
"Let me caution you, the government, that it will be struck down. Instead of listening to us here and making the necessary correction, you are forcing us to go about a kilometre away to another building (Supreme Court) and present (the case) to another set of individuals.
"How does it raises the esteem of Parliament? We are doing something which is hopelessly unconstitutional," the former Union Minister said, adding that the Bill should be sent to a Select Committee.
Among other key provisions, the Bill empowers the Director-General of the National Investigation Agency (NIA) to grant approval for seizure or attachment of property when a case is being investigated by the agency.
The existing law requires the investigating officer to obtain prior approval of the state police chief to seize properties linked to terrorism.
The government is of the view that on many occasions, terror accused own properties in different states. In such circumstances, seeking approval of state police chiefs causes delay and hampers investigation.
While the Congress has endorsed most amendments in the Bill, it stoutly opposed the clause that empowers the government to designate an individual as terrorist.
Chidambaram said that Pakistan-based Lashkar chief Hafiz Saeed and activist Gautam Navlakha, who has been arrested for the Bhima Koregaon violence, cannot be compared.
Home Minister Shah clarified that a person cannot be designated a terrorist on assumption and belief as argued by the opposition leaders. He said there would be a four-stage scrutiny before any individual is tagged as a terrorist.
Speaking first on the Bill, Elamaram Kareem of the CPI-M opposed it. He said that in the name of combating terrorism, the government was imposing state terrorism on people.
"Home Ministry will have the authority to declare a terrorist in any state and need not inform the concerned state government. This is the new model of cooperative federalism. The properties of such identified people will be confiscated.
"Individuals expressing dissent can now be declared as terrorist arbitrarily. The principle of jurisprudence has been turned upside down by placing on the person on whom allegations are made to prove his or her innocence," Kareem said.
( With inputs from IANS )