Wales and Northern Ireland Secretary Peter Hain says he rumbled Rory Bremner quickly when the impressionist called him pretending to be Gordon Brown.
Bremner admits he was caught out when he asked Mr Hain about Welsh elections.
But while Mr Hain praised Bremner, he also accused him of "spreading cynicism and embitterment" about politicians.
They clashed after it emerged Bremner had tricked Foreign Secretary Margaret Beckett into a conversation while he was impersonating Chancellor Mr Brown.
The comedian and Mr Hain fell out on BBC One's Sunday AM after details were revealed of Bremner getting Mrs Beckett to discuss her Cabinet colleagues on the day of the 2005 general election.
Bremner told presenter Andrew Marr how Mrs Beckett had spoken to him as "Gordon Brown".
However, she said she had no recollection of the conversation, and called it an "unprincipled and unpleasant breach of privacy."
Mr Hain also went on the attack when he accused Bremner of questioning his principles.
It came after Bremner told the programme of his "spectacular failure" in phoning Mr Hain a couple of days before the call to Mrs Beckett.
Bremner said: "I had a conversation about the Welsh elections and, after about a minute in, the line went very quiet and he (Mr Hain) said: 'You're not really Gordon Brown, are you?'
"At which point the ground opened beneath my feet and I thought, well I've got to keep bluffing.
"So I said (as Mr Brown), 'Come on Peter, for heaven's sake, we've got an election to fight. Can we not be serious?' And he said, 'yeah, very good try.'
"So I hung up and I thought the only thing to do is to ring him back as Tony Blair.
"So I said (as Mr Blair), ' Peter, have you just had a call from someone pretending to be Gordon Brown? And he said 'yeah, nice try.' "
Mr Hain told the programme that he had realised quickly that he was not talking to the chancellor.
The Neath MP said while Bremner's impersonations were "terrific" and made him "laugh like hell", he should stop "spreading cynicism and embitterment about politicians."
But Bremner questioned Mr Hain's views on renewing Britain's nuclear weapons and the Iraq war and said: "I want to know who's impersonating Peter Hain, because I remember you as this left wing and ideological figure."
Mr Hain responded: "And I'm very proud of that, Rory. Don't disparage.
"You do a great job in breeding cynicism and knocking down everybody. That's your job, fine.
"But don't start making accusations. I've kept to my principles. I'm proud of what I've done in the past."
Mr Hain said he would not question Bremner's honesty or principles. "Let's have a bit of fair play and give and take," he added.