The YouGov daily survey for The Sun suggested the contest had become a real three-horse race, with the Lib Dems on 30 per cent to Labour's 28 per cent and the Conservatives in the lead on 33 per cent.
Mr Clegg's party leapt ahead eight points compared with the previous day, taking four points from the Conservatives, three from Labour and one from other parties in the poll, conducted after the historic 90-minute debate was broadcast on ITV1.
Today's poll is the second to show a surge of support for Lib Dems in the wake of the debate, following an ITV/ComRes survey yesterday which put the party up three points to 24 per cent, but still trailing Labour on 28 per cent and the Tories on 35 per cent.
It indicates that the first televised leaders' debate in British General Election history may have blown the race for 10 Downing Street wide open.
Not since the days of the SDP/Liberal Alliance in the 1980s have Labour been forced into third place in national polls of this kind.
Polling evidence suggests that the swing to the Liberal Democrats is even stronger among the 10 million voters who tuned in to watch Thursday's debate.
The ITV/ComRes survey found that, of a sample of 4,000 viewers who watched the broadcast, some 35 per cent said they would vote Lib Dem, against 36 per cent for the Tories and 24 per cent for Labour.
And Mr Clegg was picked as the winner of the debate in four separate instant surveys, racking up support as high as 61 per cent in one poll.
The Lib Dem leader will focus on health policy today as he and his wife Miriam, in a rare joint appearance on the campaign trail, visits the south London hospital where one of their sons was born.
Thanks to the complexities of the Westminster voting system, the figures in The Sun poll may be more disastrous for the Tories than for Labour.
According to the BBC's election seat calculator, if repeated on an even swing across the country on May 6, they would produce a hung Parliament with Labour the largest single party with 276 MPs against 246 Tories and 99 Lib Dems.
Such a result - coupled with Mr Clegg's role as "kingmaker" - would be certain to increase the pressure for electoral reform.
Observers will now be keenly watching to see whether the Lib Dems' dramatic surge in support is repeated in later surveys. With a three-point margin for error in most polls, statisticians are always keenly aware that an individual poll may simply represent a freak result, rather than a genuine trend in public opinion.
Today's development will mean the spotlight is very much on Mr Clegg as he continues his election campaign, and particularly when he squares up again with Gordon Brown and David Cameron for next Thursday's debate on Sky News.
Over the past 24 hours, Tories have launched a sustained attack on the Liberal Democrats' "eccentric" policies in a bid to offset the impact of Mr Clegg's TV performance, while Labour responded by underlining how close they were on some key issues with the third party.
Shadow chief treasury secretary Philip Hammond last night said Mr Clegg had successfully presented himself as the "outsider" in the debate, but predicted that voters' enthusiasm for Lib Dems would wane as their policies were put under scrutiny.
The election would not be judged like a "sixth-form debating contest", he said.
Mr Hammond told BBC2's Newsnight: "What people will want to look at now is the Lib Dem policy on areas like crime, immigration, defence, Europe, and when they come to look more closely at what Liberal Democrat policies actually are, they will find they are not quite as Nick Clegg was presenting them."
Labour's Schools Secretary Ed Balls said that previous Lib Dem leaders like Paddy Ashdown and Charles Kennedy had enjoyed a surge in the polls early in an election campaign as they began to receive more media attention than they were used to.
But he said that the key message from the debate was that Mr Cameron had been wrong to think he was heading for certain victory.
"He has been completely exposed," said Mr Balls. "Nick Clegg did well in the debate, Gordon Brown defined the question for the election which is how we secure the recovery, but David Cameron was completely knocked off course."
Mr Balls suggested that while Labour had "some differences" with the Lib Dems on policy, the two parties had more in common with one another than with the Conservatives.
Lib Dem foreign affairs spokesman Ed Davey told Newsnight: "Nick had a very good performance. That's given us a boost, but we know we have got a hard job over the next few weeks to turn that into massive Liberal Democrat success."
* YouGov polled 1,290 adults for The Sun on April 16.
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