Nick Clegg has accused Nigel Farage of peddling "dangerous fantasies" in an ill-tempered BBC TV debate on Britain's future in Europe.
Mr Farage accused the Lib Dem leader of "wilfully lying" to the British people about Brussels' grip on UK laws.
He also claimed EU immigration had hit the "white working class" the hardest.
Instant polls said Mr Farage had won by a bigger margin than he did in their first debate last week.
YouGov's snap poll gives the debate to Mr Farage by 68% to 27%, while a poll by ICM/Guardian suggested 69% of people watching thought the UKIP man came out on top.
A YouGov/Sun poll suggested Mr Farage won their first clash last Wednesday by 57% to 36%.
The BBC's chief political correspondent Norman Smith said Mr Clegg was much more fired up than he had been last week, while Mr Farage had been more measured.
'Billy no mates'
Mr Clegg kicked off the one-hour debate - hosted by David Dimbleby - by accusing his opponent of foisting a "dangerous con" on the public by arguing for Britain's exit from the EU, telling the audience in the BBC's radio theatre "if it sounds too good to be true, it is".
He warned leaving the EU would lead to a 'Billy-no-mates Britain".
An early flashpoint was Mr Farage's support for Vladimir Putin over Syria.
The UKIP leader accused the Lib Dem leader of being "hell bent" on getting Britain involved in a war - but Mr Clegg accused him of trivialising the issue.
Mr Clegg also said Mr Farage's views on Mr Putin were reminiscent of a "pub bar discussion" - and that the Russian leader could have brought the conflict in Syria to an end with "one phone call".
Poking fun at Mr Farage, the Lib Dem leader suggested the UKIP leader would claim next that "the moon landing never happened, Barack Obama is not American and Elvis is not dead".
Mr Farage said the British people had "had enough of getting involved in foreign wars".
'Making things up'
He said he did not want Britain to be part of an "expansionist" EU foreign policy, claiming that the EU wants its own "army and navy".
Mr Clegg said this was a "dangerous fantasy that is simply not true".
The pair traded verbal blows over the percentage of British laws made in Brussels, with Mr Clegg claiming it was only about 7%. He also said the European Commission only employed about the same number of people as Derbyshire County Council.
Mr Farage told the Lib Dem leader: "When I said yes to these debates I thought you would honestly make the pro-EU case.
"By saying 7% of our laws are made in Brussels, you are wilfully lying to the British people about the extent to which we have given control of our country and our democracy and I am really shocked and surprised you would do that."
Mr Clegg hit back, accusing the UKIP leader of "making things up to make a point".
The pair again clashed on EU immigration, with Mr Farage saying it was "good for the rich because it's cheaper nannies and cheaper chauffeurs and cheaper gardeners but it's bad news for ordinary Britons".
The UKIP leader said the scale of immigration over recent years had "shocked" the country and increased segregation in towns and cities.
But he said the worst social impact was that "it has left the white working class effectively as an underclass, and I think that is a disaster for our society".
The Lib Dem leader suggested that Mr Farage "does not like modern Britain" and that, in contrast, he was very comfortable with it.
Mr Clegg attempted to mock the UKIP leader as someone who was not a serious politician.
At one point, he brandished a UKIP leaflet - featuring a picture of a Native American - which he said suggests that if the British people ignore immigration, they will "end up on a reservation".
"What are you going to say next, that you are Crazy Horse or Sitting Bull?," he asked.
Mr Farage said he did not "recognise" the leaflet and did not "endorse its sentiments".
The Lib Dem later claimed the leaflet was distributed in Lancaster and Fleetwood ahead of the 2010 election but UKIP said it was not "official" party literature.
Towards the end of the debate, the UKIP leader issued a warning about the rise of far right parties in Europe, saying: "I want the EU to end but I want it to end democratically. If it doesn't end democratically I'm afraid it will end very unpleasantly."
He used his closing statement to make a pitch for votes in May's European elections, saying: "Let's free ourselves up and in doing so let's give an example to the rest of Europe.
"I know the people are behind this. I would urge people - come and join the people's army. Let's topple the establishment who got us into this mess."
Mr Clegg sketched out a vision of Britain's future in Europe entirely at odds with his Eurosceptic opponent in his closing remarks, promising "real remedies for the way the world is today not dangerous fantasies about a bygone world that no longer exists
"And that is why I'm going to do everything I can to make sure that we remain part of the European Union because that is how we protect the Britain we love."
Conservative leader David Cameron and Labour leader Ed Miliband declined to take part in the debate.
Tory defence minister Anna Soubry said Mr Clegg backed the status quo in Europe while Nigel Farage could not deliver the change the British public wanted.
In contrast, she said the Conservatives were "absolutely united in our desire to renegotiate with Europe and to have a referendum - and to trust the British people to make up their minds".
For Labour, shadow attorney general Emily Thornberry said voters were more concerned about "making ends meet" than the future of Europe and the party's focus was on securing a debate between Mr Cameron and Mr Miliband in the run-up to next year's general election.
The SNP said it believed in "positive engagement" with the EU and an independent Scotland would have "a seat at the top table in Europe".
Plaid Cymru said it wanted a "strong voice" for Wales at the heart of Brussels and it was concerned that Wales could be "pulled out of the EU against its own will and its own interests".