Jubilant Lib Dems hailed their leader's performance, saying it could transform the General Election battle, giving them the momentum to overhaul Labour's second place in the opinion polls.
But the Conservatives made clear they intended to target the party in the run up to the second debate next week, when Mr Clegg will again go head-to-head with David Cameron and Gordon Brown.
A strong Lib Dem performance on polling day would increase the chances of a hung parliament, reducing the prospects of the Conservatives being able to form a majority government.
The importance of the debates was underlined by viewing figures which showed a peak audience 9.9 million tuned in for the 90 minute encounter on ITV1 - beating even Coronation Street which immediately preceded it.
Mr Cameron accepted his Lib Dem rival had had a "good debate" but insisted the Tories could still triumph on polling day.
"It's a huge challenge," he said in a phone-in on BBC Radio Manchester.
"We are in the middle of a hard-fought and tough election campaign. It's a campaign I believe we can win. It's a campaign I believe we ought to win because the country is crying out for change."
His shadow children's secretary Michael Gove warned they now intended to subject the Lib Dem's policy programme to intense scrutiny.
He highlighted Lib Dem plans to join the euro, scrap the Trident nuclear deterrent and offer an amnesty to illegal immigrants, which, he said, lay well outside the political mainstream.
"The greater degree of scrutiny these policies have, the more that people will realise that while Nick Clegg is a very attractive individual in many ways, the policies of his party are outside the mainstream and a little bit eccentric - not necessarily what you would want at a time of crisis and difficulty," he told Sky News.
"Nick Clegg can play the role of the sparky and feisty outsider, the new kid on the block - and he plays that with a degree of assurance - but if you are making a decision about who the prime minister is, it is more important to weigh in the balance policy decisions."
In contrast, Labour was keen to emphasise areas of agreement with the Lib Dems, with Home Secretary Alan Johnson pointing to their opposition to push through spending cuts this year.
"Cameron and Osborne almost alone in Western politics believe you cut at the height of a recession. We agree with the Lib Dems on that," he told the BBC.
"We agree also on the need for really substantial reforms to our constitution - electoral reform in particular."
Mr Clegg, on the campaign trail in Warrington, was anxious to damp down expectations following the debate, saying it had been an "important moment" but stressing there was still a long way to go.
"It is just the beginning, but there is quite a way to go until people have their say in the ballot box. The leader's debate was an important step, but it was the beginning of the campaign proper," he said.
Lib Dem foreign affairs spokesman Edward Davey said Mr Clegg's strong showing in the debate could give the party a lift which could see it overtake Labour in the polls.
"I'm not necessarily saying it's going to happen, but it's possible this will completely change this election campaign," he told the BBC.
"If we see polls with the Liberal Democrats catching up on Labour, and even overtaking them, that is going to give us the momentum."
Mr Clegg topped four instant polls in the hours after the broadcast, claiming 51% of viewers' votes in a survey for The Sun, 43% in another for ITV News and 37% in a text message poll for Sky News.
The Sun had Mr Cameron on 29% and Mr Brown on 19%, ITV1's poll scored them on 26% and 20% respectively and the Sky News survey put the Tory leader marginally behind the Prime Minister by 31% to 32%.
In The Times, the Lib Dem leader was rated the winner by a colossal 61%, against 22% for Mr Cameron and 17% for Mr Brown.
Transport Secretary Lord Adonis later played down the Liberal Democrats' success in instant opinion polls, insisting that the choice was between a Labour or Conservative government.
He told BBC Radio 4's World At One: "We're fighting for every vote and seat, of course we are, and we'll continue to do so and the next two debates will be a crucial part as that.
"So far as the Lib Dems are concerned, of course, across most of the country they are the third party and the issue facing Lib Dem voters is whether they wish to see a Labour government after May 6 or a Conservative government."
He said the policies of Labour and Liberal Democrats were "very close together".
"The Lib Dems start as the third party. Lib Dem voters by voting Lib Dem of course simply make it more likely that the Conservatives will get in as against the Labour Party...
"These are issues that voters will need to weigh as they watch the debate."
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