Mr Clarke, the 65-year-old former chancellor emerged as the winner of the party's "generation game" after competing with David Cameron, the 38-year-old shadow Education Secretary, to claim the status of main challenger to Mr Davis.
There were signs of nervousness among supporters of Mr Davis after Mr Clarke, the party's self-styled "big beast" won a genuinely warm response from Tory activists who appeared ready to cast aside their doubts about his pro-European views.
A strong performance by Mr Cameron added to the pressure on Mr Davis to bolster his position as favourite when he addresses the conference today. "He has everything to lose," one ally admitted.
Mr Davis, the shadow Home Secretary, will reject calls by Conservative modernisers for the Tories to accept radical change to become electable. Instead, he will tell the party to feel good about itself.
"Let's walk tall - let's stop apologising and get on with the job," he will tell the conference. Pleading for party unity, he will tell the opposing camps in the leadership race to stop sniping at each other. "Our goal as a party is power but power with a moral purpose," he will say.
Mr Davis is expected to play to a more traditional right-wing agenda when he makes a second speech to the Thatcherite Conservative Way Forward dinner tonight. Last night he backed right-wing demands for a cut in the upper time limit for abortion from 24 weeks to 14 or 12 weeks.
Allies of Mr Clarke were delighted by the standing ovation he won. His response fuelled speculation that he could face a "stop Clarke" operation by Davis supporters aimed at ensuring Tory MPs do not vote him on to the shortlist of two from which the party's 300,000 members will choose the new leader.
The former chancellor avoided all mention of Europe but unveiled his unique selling point as the man who could beat Gordon Brown at the next election. Saying that Mr Brown's economic legacy would haunt him after he succeeded Tony Blair as Prime Minister, Mr Clarke promised: "I'll make sure of that."
Mr Clarke sought to portray himself as in the mainstream of his own party, recalling that he had cut taxes and the share of national income taken by public spending when he was Chancellor.
The Cameron camp insisted the race was still wide open and contrasted what they called a "backward-looking" address by Mr Clarke with Mr Cameron's ability to lead the party into a "new generation" and to appeal to a new generation of voters. Allies of Mr Cameron believe his assured conference performance will give him crucial momentum when Conservative MPs hold the first round of their ballot on 18 October. Before then, he will try to win over MPs at one-to-one meetings and send them polling evidence that he - rather than Mr Clarke - is best-placed to win back lost Tory voters.
The bookmaker William Hill reported a huge gamble on Mr Cameron, forcing his odds down from 10/1 to 4/1 third favourite.
More than £1m in bets is riding on the outcome of the leadership election. Mr Davis remains the 1/2 favourite while Mr Clarke is the 11/4 second favourite, followed by Mr Cameron, Liam Fox at 14/1 and Malcolm Rifkind at 50/1.
More candidates could yet enter the race. The right-wing Cornerstone group is seeking more concessions from Mr Fox and Mr Davis before announcing whether it will run its own candidate against them.
Mr Fox's threat to back the withdrawal of Britain from the EU was seen by members of the group as a sign it was extracting commitments that otherwise would not have been made.
Michael Ancram, the shadow Defence Secretary, will decide today whether to stand after hearing Mr Fox speak from the platform.
Edward Leigh, a member of Cornerstone, said he would decide next Tuesday whether or not to stand. "There is everything to gain by leaving it to the last moment. We have got to see what the other candidates say including Liam Fox," said Mr Leigh. "We've had one of the candidates already saying he is prepared to consider withdrawing from Europe.
"We think it's a good idea to have a radical right manifesto with education vouchers and flat tax and then you can get a block of votes behind it."
Cameron: 'We'll be tested and challenged'
Portraying himself as young, passionate and energetic, David Cameron promised the Tory faithful that he could help them to cross the generation gap among voters.
The 38-year-old shadow Education Secretary said he was the man to win back missing voters - particularly younger electors, where the Tories are lying third in popular support - as he set out his vision of "modern compassionate Conservatism".
He dismissed suggestions that the Tories would win power with "one more heave" or by moving to the right. And he echoed Margaret Thatcher as he told the conference: "I want you to come with me. We'll be tested and challenged. But we'll never give up, we'll never turn back."
Joined on stage by his wife, Samantha, he won a three-minute standing ovation for his speech, delivered without notes. His campaign team will now be keen to turn the warmth of his reception on the conference floor to firm pledges of support from MPs when the Commons returns next week.
Mr Cameron said the party could take no satisfaction from its slow progress at the last election. "Let's resolve here, at this conference, when we put defeat behind us, failure behind us, to look ourselves in the eye and say: 'Never, ever again.'"
"There is a new generation of businessmen and women who are taking on the world, creating the wealth and opportunity for our future.
"We can lead that generation - we can be that new generation."
David Cameron, 38
Time: 19 minutes, 55 seconds
Rounds of applause: 20
Buzzwords: "Modernise" 1, "Young" 6, "Change" 10, "Win" 2.
Best joke: (of Gordon Brown) "How are we going to stop him? Tony Blair can't. God knows, he's tried hard enough"
Best soundbite: "I want you to come with me. We will be tested and challenged. But we will never give up, we will never turn back."
Style: Sharp dark grey, single-breasted designer suit. Cream shirt and fashionable shiny gold silk tie
Delivery: Stood alone on the platform, speaking without notes (but was seen practising the speech to an empty hall the day before)
Ovation: Just over three minutes (but he milked it to the end).
Clarke: 'Low taxation will be the prize'
A confident Kenneth Clarke portrayed himself as the only man who could beat Gordon Brown at the next election.
Pleading for support from the party that rejected him in its 1997 and 2001 leadership elections, Mr Clarke told the conference: "The question we have to answer is: do we really want to win?"
He said the Tories needed to choose "an even bigger beast" than Tony Blair or Mr Brown in order to push Labour out at the next election. Saying that modernisation was not enough, he argued: "You can have marvellous policies on every other subject, but if you do not win the argument on the economy, you are sunk. I do not have to prove my economic competence to the British public. I won my reputation over four years as Chancellor."
He pledged to commit the Tories to reduce the share of national income taken by public spending from the current 42 per cent to 40 per cent.
Mr Clarke insisted that the Tories were united on the merits of a "low tax economy", but he differed with the leadership front-runner, David Davis, by saying tax cuts would "not be easy", would be "miles away", and that public services had to be safeguarded.
He described Mr Blair as "a huge political cuckoo" in the Tory nest, but concentrated his fire on Mr Brown, saying he had "blown" the good "inheritance" he enjoyed after Mr Clarke's spell at the Treasury. He predicted that Mr Brown's own economic legacy "will haunt him".
Kenneth Clarke, 65
Time: 23 minutes 44 seconds
Rounds of applause: 20
Buzzwords: Chancellor 3, Beast 2, Lose 1, Win 3
Best joke: "We are searching for a leader who will be seen by the public as a prime minister in waiting. Well, oh boy, have you kept me waiting."
Best soundbite: "Gordon Brown told the Labour Party conference that they were going to dominate the centre ground. Oh no they are not. The time has come to take back the political ground that should be ours."
Style: Light grey, trademark double-breasted suit, green striped shirt and red and blue patterned tie.
Delivery: Stood behind the podium, with prepared text.
Ovation: Just under two minutes (but he left delegates on their feet).