David Cameron and Ed Miliband have been put on the spot over immigration, the EU and spending plans in the first set-piece TV broadcast of the election.
The PM said he had "turned the economy around" while the Labour leader said he was "tough enough" to be PM.
Jeremy Paxman began the Channel 4/Sky programme by grilling Mr Cameron about food banks and zero hours contracts.
Mr Miliband said his relationship with brother David was "healing" after their bruising leadership battle.
At the end of Mr Miliband's interview, host Paxman was caught on microphone: "Are you OK, Ed?"
The programme was not a direct debate between the two leaders. Rather, each man faced a separate interview with Channel 4's Paxman and also answered questions from a studio audience, moderated by Sky's Kay Burley.
'Manageable and doable'
It attracted an audience of 2.6 million viewers - around 11.7% of the UK television audience - on Channel 4. This compared with about nine million for the first TV debate at the 2010 election. The viewing figures for Sky are yet to be released.
The debate also proved popular on social media, with the #BattleForNumber10 reaching the top of Twitter's trending list in both the UK and worldwide.
Both parties claimed afterwards that their man did best, but an early ICM opinion poll for the Guardian suggested Mr Cameron shaded it, with 54% of of the 1,123 viewers surveyed saying they thought the PM "won".
Launching Labour's election campaign on Friday, Mr Miliband brought up the previous night's debate, which he said had shown Mr Cameron to be "a rattled prime minister running from his record".
He said the prime minister's answers to questions on food banks and exclusive zero hours contracts showed he was "living in a different world".
By Ross Hawkins, BBC political correspondent
Ed Miliband might just have acquired a catchphrase.
The Labour leader who Jeremy Paxman dubbed a "north London geek" borrowed the argot of a Wild West gunslinger when he came out to confront questions about his character during the first of the leaders' TV specials.
When Paxman - the grand alpha-male of political interviewing - leaned in, so too did Miliband.
"That's why Cameron didn't want to debate him," one Labour aide declared, at volume, as he entered the post-show spin room.
Earlier, Labour's general election co-ordinator Douglas Alexander renewed the party's challenge to the prime minister to face Mr Miliband in a head-to-head TV debate.
He said last night showed why Mr Cameron was "so unwilling" to have that debate - but urged him to reconsider, "even at this late hour".
But Conservative Party chairman Grant Shapps told the BBC: "Surely by now we should be on to discussing the issues at stake, rather than the format of these debates."
Appearing first, Mr Cameron said he wanted an economy "that does not just look good on the page", and said he could not live on an exclusive zero hours contract, of the kind the coalition government has banned.
He also said:
- When he spoke in support of fired Top Gear presenter Jeremy Clarkson, he had not known what had happened
- He had given an "honest answer to an honest question" when he said he would not seek a third term as prime minister
- A Conservative government would be able to find a further £10bn in welfare savings, but would not specify where they would be made.
Asked by an audience member how severe future spending cuts would be, Mr Cameron said they would be "manageable and doable", but that "efficiencies" would be needed.
Mr Miliband, when asked by Paxman whether he was tough enough to be prime minister, responded "hell yes", before adding: "Let them underestimate me".
He said he was "not going to get into a bargaining game" with the SNP's Alex Salmond and that public spending was "likely" to fall under Labour.
During the audience question-and-answer session, he said he believed wealth creation was "incredibly important".
Mr Miliband, who is set to officially launch Labour's campaign with a speech at the site of the London Olympics on Friday, also said Labour had been "wrong" in the way it regulated the banks.
He said he did not care when Paxman said he was seen as a "North London geek" and added: "I don't care what the newspapers write about me, because what I care about is what happens to the British people, and I know that this country could be so much better."
Meanwhile in the "spin room" alongside the studio, party heavyweights and journalists watched the action before giving their version of events.
Conservative Party chairman Grant Shapps said the prime minister "came across as the man with the plan".
Labour's general election co-ordinator Douglas Alexander said Mr Miliband was seen to be "warm honest and open" and not the "caricature" that the public has "read about in the newspapers".
UKIP leader Nigel Farage, who also attended the event, thought Mr Miliband had shaded it, saying: "Taking policy out of it, on personality, for me, Miliband was ahead."
Green MP Caroline Lucas told BBC News it was a "pretty even contest" but added that there was a sense of "disappointment" that the "real issues" of the election "were not properly aired".
Asked who her party would support in the event of the election producing no overall winner, she reiterated that the party would be open to an informal "case by case" deal a minority Labour government.
- 26 March: Live question-and-answer programme on Channel 4 and Sky News featuring David Cameron and Ed Miliband, presented by Jeremy Paxman and Kay Burley
- 2 April: Debate with seven party leaders on ITV, moderated by Julie Etchingham
- 16 April: Debate between five opposition party leaders on the BBC, moderated by David Dimbleby
- 30 April: BBC Question Time programme with David Cameron, Ed Miliband and Nick Clegg, presented by David Dimbleby
The programme - Cameron and Miliband Live: The Battle for Number 10 - was the first of a series of television events agreed by the broadcasters and political parties following protracted negotiations.
Thursday's broadcast has been the subject of hundreds of complaints about alleged bias against the Labour leader.
Ofcom said it had received 131 complaints, and would assess them before taking a decision on whether to investigate.
A Channel 4 spokeswoman said it had received around 300 complaints - but did not specify what they were about.
She added: "Both politicians, one of whom is likely to be the next prime minister, agreed to the format and were prepared for and actively participated in robust questioning about their policies and abilities. Neither party has expressed any dissatisfaction to Channel 4."
Mr Cameron, Mr Miliband and Liberal Democrat leader Nick Clegg will feature separately in a BBC Question Time special on 30 April, just a week before the nation goes to the polls.