The PM said he had rejected Â£8bn in child benefit cuts the Lib Dems claimed the Tories had proposed in government.
Ed Miliband said Labour did not overspend when in power and that he would not lead a government if it involved a deal with the SNP.
Nick Clegg was grilled over tuition fees, trust and coalition deals.
While insisting they could both win outright, the Conservative and Labour leaders gave the clearest indications to date of the terms of possible post-election deals, with Mr Cameron saying his pledge of an EU referendum in 2017 would be a "red line" in any negotiations.
Three other leaders also faced audience questions:
The prime minister was first in the firing line at Leeds Town Hall.
Mr Cameron said he did not want to cut child benefit or child tax credits if he won the election, but that it was possible to save more from the welfare budget.
Asked if this amounted to an "absolute guarantee," he said child tax credit "would not fall" and child benefit was "one of the most important benefits there is" and did not need to change.
Brandishing the note left in 2010 by outgoing Labour Treasury Secretary Liam Byrne, stating there was "no money left", Mr Cameron said:  "It takes a long time to fix the mess that I was left."
"We are half way through a building job," the PM added.
Asked if his vow to pass laws preventing tax rises was an admission he usually lied, Mr Cameron said he wanted to put the policy "beyond doubt".
He said he had not agreed to a head-to-head debate with Mr Miliband because: "This, giving you the chance to answer questions directly, this is more powerful than a televised debate."
Mr Cameron was then asked why people did not trust the Conservatives on the NHS, replying that improving the health service was "my life's work" but only possible with a strong economy.
He refused to speculate on what might happen in the event of a hung Parliament, saying he did not want to do a deal in a "darkened room with Nick Clegg", but said an in/out referendum on the EU would be a "red line" in any coalition negotiations.
The Labour leader said nothing he has not said repeatedly before - explaining his view that the deficit resulted from the financial crash and not from over spending by the last Labour government. He gave no new hostages to fortune but it was, nevertheless, the toughest ride he's faced in this campaign.
With David Cameron looking confident the Tories and the Tory press will claim that this was the night the election turned.
But - and it is a big but - the prime minister's performance relied on either ignoring or dodging the hostile questioning he faced about welfare cuts, the bedroom tax, food banks and the morality of his policies.
Read more from Nick
Read Carole Walker's leader-by-leader analysis.
Ed Miliband faced tough questions, with one man accusing the Labour leader of lying and telling him it was "absolutely ludicrous" to suggest his party had not spent too much in government.
Mr Miliband said: "There was a global financial crisis, there was a high deficit. That deficit has not been cleared. It will be the mission of my government to cut the deficit every year and balance the books."
He dismissed Liam Byrne's letter as Mr Cameron's "regular prop".
Mr Miliband then rejected the PM's claim that the Conservatives would not cut child tax credits. The issue was "on the ballot paper" in light of Mr Cameron's earlier response, he suggested.
On the prospect of a post-election deal with the SNP, he said: "If the price of having a Labour government was a deal or a coalition with the Scottish National Party then it is not going to happen."
ComRes, having registered Conservative leads in its three earlier campaign polls, put them neck-and-neck with Labour on 35% each this time. YouGov suggested a one-point Conservative lead (35% versus 34%).
However, the drama came with Mori's five-point Conservative lead - 35% as against 30% for Labour.
Some interest was aroused when its entrails revealed 63% of 2010 Labour voters remaining loyal to the party, compared with much higher numbers in other polls. A breakthrough for the Conservative campaign or a detail that provokes doubt about the findings? I suspect the latter, but we shall see.
The instant ICM poll assessing the performances of the three leaders on Question Time suggested 44% thought David Cameron had come out on top, compared with 38% who nominated Ed Miliband and 19% Nick Clegg.
No game-changing campaign moment here, it seems. Oh well, back to the national polls we go.
He also ruled out a "confidence and supply" arrangement, with his party trying to win SNP support on an issue-by-issue basis.
What are the top issues for each political party at the 2015 general election?
Policy guide: Where the parties stand
"I am not going to start bartering away my manifesto, whatever the outcome of the election," he added.
Mr Miliband refused to set an immigration target, telling one questioner: "I don't want to stand on this stage in five years time and explain why I have broken my promise."
As he walked off stage when his half-hour was up, the Labour leader briefly lost his footing - something that was seized on by his critics in the press.
Nick Clegg was immediately quizzed about the Lib Dems' U-turn on tuition fees.
He then faced pointed questions about why his party had not revealed an alleged Conservative proposal to cut child tax credits on Thursday earlier.
Mr Clegg said the Conservatives had "a very unfair plan to balance the books, which departs from what we've done in coalition and I think we are entitled to say: 'What are you going to do? Who are you going to hurt?'".
The Lib Dem leader defended his decision to go into coalition with the Conservatives in 2010, after an angry former Lib Dem voter said he would have preferred a deal with Labour. Mr Clegg said it had been the "democratic" thing to do so and a "plucky and brave way to put country before party".
However, Mr Clegg said that this year he had been "much clearer" on the "red lines" he would insist upon in any coalition negotiations with Labour or the Conservatives, such as a requirement for education spending to increase by Â£5bn by 2020.
He indicated he would seek to form another coalition with the party that got the most seats in next Thursday's general election.
But Mr Clegg said he would only back an EU referendum if more powers were handed to Brussels, potentially putting him at odds with Mr Cameron.
At one stage an audience member asked if he had plans to find a new job when he became unemployed next week. "No I don't," the Lib Dem shot back.
Mr Clegg managed a quip at the expense his rivals, saying: "He (David Cameron) keeps talking about darkened rooms, as does Ed Miliband.
"If either of them still think they are going to win a majority they need to go and lie down in that darkened room."
An instant poll of Question Time viewers conducted by ICM for The Guardian found that 44% thought Mr Cameron had "done best", against 38% for Mr Miliband and 19% for Mr Clegg.
Responding to the Question Time show, Green Party Natalie Bennett - who was not invited to appear in a TV event - said each of the three leaders signed up to the "many facets of business-as-usual politics".
The event was "a clear example of why we urgently need a real alternative in British politics", she said, arguing that none of those appearing in the event offered "a genuine alternative to the failed policy of austerity".
"No-one was truly standing up the vicious rhetoric on immigration that has infected political debate in this country," she added.
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David Cameron and Ed Miliband have faced tough questions from a Question Time audience over their economic plans in the final TV event of the campaign.