The leadership favourite, not known as a strong speaker, came to his key conference speech with everything to lose.
Rivals David Cameron and Ken Clarke raised the stakes with powerful platform addresses yesterday.
But Mr Davis insisted it was he who could bring together the party and country in what was billed as a leader's, rather than a leadership, speech.
"I'm proud to be a Conservative, proud of our history, proud of what we achieved for our country," he said.
"I will not concede defeat to Gordon Brown and Tony Blair. I don't believe that our best days are behind us.
"I believe that the best is yet to come."
The shadow home secretary's speech contained rebuffs to both his main challengers.
Former Chancellor Mr Clarke insists his pro-Europe views should not be an issue in the contest.
Mr Davis said: "The issue of Europe hasn't gone away, and it's not about to. The drive to deeper integration never rests.
"So ask yourself this; if the Conservative Party doesn't speak up for Britain's interests, then who will?"
Shadow education secretary Mr Cameron yesterday urged activists to admit past failures and modernise the party to win.
Mr Davis said: "Yes. We need debate about our future. Yes. We need to agree on change. But we don't need a collective nervous breakdown.
"So let's stop apologising - and get on with the job."
Not as polished as his two chief rivals, a couple of rows of activists remained firmly in seats while others gave him an ovation.
Liam Fox will be the last declared contender to deliver his conference speech this afternoon.
However, deputy leader Michael Ancram will announce whether he is entering the race when he gives the final address of the day.
With 66 public pledges from MPs, Mr Davis should be guaranteed a place in that contest but admitted ahead of his speech "that doesn't matter".
"This is not over until it is over and the last round - which I expect to be in - will be with the party in the country and they have got to make up their mind what sort of party they want," he said.
The shadow home secretary acknowledged Mr Clarke would be a "formidable" opponent if he made the final membership ballot but insisted he was pleased the former Chancellor was standing.
"I thought he would elevate the contest. He has. He will continue to do so but I still think I can beat him," he said.
Mr Cameron said today that there was "a lot of work to do" if he was to win a place in the final run-off to succeed Michael Howard.
"What I have to do is convince MPs - and there are a lot among the new intake particularly who have yet to make up their mind - that I really can do it, that I have got the right ideas, that I can take the party forward," he said.
"I had very good response to my speech yesterday. We had three new MPs, who I wasn't expecting necessarily to come in support, and they are supporting me. There will be a couple more later this week.
"I think Ken Clarke has a good level of support amongst people who have known him for a very long time. He has been in Parliament for 30 years. I've got to prove to people that I can do it.
"I made a great step forward yesterday. There is a lot of work to do but I can get into that last two and I think if I take my message round the country, it will be very popular."
Sir Malcolm Rifkind, the trailing leadership contender, hailed Mr Clarke as "very able and great guy" but warned his pro-Europe views meant some Tories had "very great reservations" about him.
"It is up to him to prove that he can lead a united party. That is where the question exists. It does not exist in my case," he told BBC Breakfast.
Sir Malcolm is tipped to back former Cabinet colleague Mr Clarke when he is knocked out, but insisted he had not given the issue any thought.
"If you are a candidate in a campaign you fight it through, you argue your case, you fight the good fight and hopefully you win.
"If at the end of the day you don't, then you have plenty of time to think of the alternatives."Reuse content