MPs have overturned a change made by the Lords that would have blocked "fast-track" extraditions to the US.
The Lords had wanted to block 'fast-track' extraditions
They also blocked a second change to the Police and Justice Bill calling for extradition only if a trial abroad was in the "interests of justice".
Home Office Minister Joan Ryan had said the Lords' amendment would "wreck our ability" to bring fugitives to justice.
The vote follows the controversy over the extradition of three UK bankers - the "NatWest Three" - on fraud charges.
In the "fast-track" vote MPs backed the government by 320 to 263, while in the second vote, they voted 313 in support of the government and 272 against, including 14 Labour rebels.
Peers had wanted the US removed from the list of approved countries from which prima facie evidence is not required before an extradition request is granted.
Critics say the US has more powers to extradite Britons than the UK has to extradite people from the States.
During Tuesday's debate, Ms Ryan said Britain was "dealing with a trusted partner with a legal system of long standing" when it came to extradition arrangements with the US.
She said: "We have extradited people to the US, and they to us, for 100 years. We trust their system just as they trust ours."
Home Secretary John Reid said he hoped the Lords would now allow the bill to proceed.
"In rejecting these amendments the Commons has given law enforcement the tools they need to fight international crime and bring serious criminals to justice in the place best able to bring them to trial.
"I hope that the Lords will now follow suit and allow our independent prosecutors to get on with their job to fight crime in the 21st century."
In the Commons, shadow home affairs minister Edward Garnier said the government's stance was "unjust, unfair, undemocratic and damaging to the interests of this country and our citizens".
The NatWest Three were extradited to the US earlier this year
Labour MP John Denham, chairman of the Home Affairs Select Committee, raised some concerns about how the 2003 extradition treaty came to be negotiated, but gave his support to the government.
Mr Denham said it had taken less than three months - from when he moved the second reading of the Extradition Bill as Home Office minister in December 2002 - for the treaty to be negotiated.
"I have to say that worries me greatly. There is every reason for modernising our extradition arrangements to the USA - it is our most important extradition partner.
"But to go from a standing start to an entire Treaty in the space of about three months...explains an awful lot about why we are where we are today."
The Liberal Democrats supported the Lords amendments, as David Heath said: "British citizens are clearly at a disadvantage in comparison with a US citizen."
The Labour rebels, plus Conservatives, had supported a letter signed by CBI director general Richard Lambert and Shami Chakrabarti, director general of human rights group Liberty, calling on Parliament to protect UK citizens from "unjust extradition proceedings".
Ms Chakrabati said: "The vote is disappointing but this campaign is just beginning. Baggage can be bundled off around the globe but people should have a little fairness first".
Conservative former Cabinet minister John Redwood criticised the US extradition arrangement.
"Where you have alleged white-collar crime ... and a situation where the person has committed no crime in Britain ... is it right they should be plucked away from their family for a very long time on a charge we don't think will go anywhere?" he demanded.
The NatWest Three - David Bermingham, Gary Mulgrew and Giles Darby - were extradited under the treaty.
It was designed to make it quicker and easier to deal with people suspected of cross-border offences such as terrorism and organised crime.
The main elements were enshrined into British law through the Extradition Act, made law in 2003, while the US Senate ratified the treaty last month.
US authorities need to outline the alleged offence, and provide "evidence or information that would justify the issue of a warrant for arrest in the UK".
However, Britain must provide the US with evidence of "probable cause", a stronger standard than "reasonable suspicion", if it wishes to extradite someone.
The NatWest Three are accused of fraud in connection with the collapse of US energy company Enron, with all three proclaiming their innocence.