The YouGov poll suggested 51 per cent of Britons believed Tory leader Mr Johnson won the debate compared to 49 per cent who favoured Labour leader Mr Corbyn.
The first head-to-head debate, which was shown on ITV, touched on Brexit, the NHS, fiscal responsibility and trust.
Those who answered “don’t know” were removed from the result, with YouGov adding the figures are so close as to be within the margin of error.
Chris Curtis, YouGov’s Political research manager, said: “Our snap poll shows that the public is divided on who won the debate, with most Labour voters thinking Jeremy Corbyn won, most Conservative voters thinking Boris Johnson won, and very few people changing their minds.
“But given the Conservatives went into this debate in the lead, they will hope the lack of a knockout blow means they can maintain this until voting day.”
YouGov added that 1,646 people were surveyed for its snap poll.
The pair clashed in front of live audience from an ITV studio in Salford, Manchester.
News at Ten presenter Julie Etchingham chaired the debate – and needed to remind both party leaders to stick to their time limits.