More than half (57%) of those surveyed following the debate hosted by LBC radio found that Eurosceptic Mr Farage had performed best.
Pro-EU Mr Clegg, who claimed during the debate that employers like Siemens would not invest in the UK if it leaves Europe, scored only 35%, according to YouGov's survey of about 1000 people.
Siemens, which employs hundreds of people in Scotland, has announced plans to create an extra 1000 jobs in Hull.
However, Mr Clegg said: "Guess what the Chief Executive of the company (Siemens) said. 'If we were not within the European Union, Siemens would make it quite difficult for me to continue to invest in UK factories'."
However, Mr Farage insisted that Mr Clegg's warnings were overblown and said that no jobs were actually in any danger.
The Liberal Democrat leader also came under pressure for a quip that people should "read the small print" on the party's previous support for an In/Out referendum on Europe - which critics accuse it of having abandoned.
Mr Farage had taken up Mr Clegg's challenge during his weekly phone-in at the London-based radio station last month.
The European elections are due to take place in May.