The Prime Minister edged a snap YouGov poll 51-49 although Labour figures were pleased with the showing of their leader in the prime-time ITV slot on Tuesday night.
The pair clashed over their rival Brexit plans, with Mr Corbyn describing the Prime Minister's pledge to "get Brexit done" by the end of January as "nonsense", while Mr Johnson suggested his rival was "not fit to lead our country".
Mr Corbyn also accused the Government of entering into secret talks with the US to open the NHS to American pharmaceutical companies in a future trade deal.
But Mr Johnson hit back, denouncing the claims as "an absolute invention", insisting there were "no circumstances whatsoever" in which a Conservative government would put the NHS "on the table" in trade talks.
He said the Labour leader was trying to disguise the "void" at the heart of his Brexit policy, which meant he was unable to say which way he would vote in Labour's planned second referendum.
He accused Mr Corbyn of being prepared to strike a deal with the SNP's Nicola Sturgeon to get the votes he needs to enter No 10 at the price of a second referendum on Scottish independence, something the Labour leader rejected.
YouGov's poll, which surveyed 1,646 viewers, also found Mr Johnson appeared more prime ministerial, although Mr Corbyn was considered more trustworthy.
The Conservatives also courted controversy for changing their Twitter handle to "factcheckUK" for the ITV debate, prompting fact-checking organisation Full Fact to label it "inappropriate and misleading".
And Mr Johnson dropped a hint about the Tory manifesto when asked if social care would be included, saying: "Yes there will and we think that nobody should pay for the cost of their social care by selling their home and everybody should have dignity and security in their old age."
Who do you think came across as more trustworthy?
40 per cent: Boris Johnson, 45 per cent: Jeremy Corbyn, 15 per cent: Don’t know
Who do you think came across as more in touch with ordinary people?
25 per cent: Boris Johnson, 59 per cent: Jeremy Corbyn, 16 per cent: Don’t know
Who do you think came across as more Prime Ministerial
54 per cent: Boris Johnson, 29 per cent: Jeremy Corbyn, 17 per cent: Don’t know
Thinking now about the debate, do you think it was right to have two leaders taking part or would it have been better with more leaders
60 per cent: Right to have two leaders taking part, 30 per cent: Would have been better with more leaders, 9 per cent: Don't mind either way, 1 per cent: Don't know
The Tory party faced criticism after one of its official Twitter accounts was rebranded as a fact checking service during the debate.
The Conservative Campaign Headquarters press office account was renamed "factcheckUK" during Tuesday evening's ITV broadcast, offering commentary on the Labour leader's statements and retweeting messages supporting Mr Johnson.
The move was criticised by independent fact-checking charity Full Fact, which tweeted: "It is inappropriate and misleading for the Conservative press office to rename their twitter account 'factcheckUK' during this debate. Please do not mistake it for an independent fact checking service such as @FullFact, @FactCheck or @FactCheckNI."
The Liberal Democrats leader said after the debate that she should have been heard in the discussions. She said "clearly” both Boris Johnson and Jeremy Corbyn “believe in Brexit”.
Ms Swinson said viewers of the showdown would be forgiven for saying they “deserve better" ahead of the General Election, adding: “the voice of Remain was not there."
Speaking to ITV after the debate, she said: "Surely we deserve than this, than what was on offer from those two tired, old parties.
The Liberal Democrats are expected to launch a fully-fledged manifesto on Wednesday, which will aim to build on a series of previously announced pledges.
These include an attempt to raise £35 billion for health and social care via a penny increase on income tax, an extra £10 billion a year on schools, a bid to recruit 20,000 more teachers, and scrapping business rates to help the high street.