The Labour leader posted the 47-second video on Twitter looking back at the 1979 no-confidence vote in James Callaghan’s government, which was one by one vote.
A total of 11 SNP MPs voted with the Conservative Party to bring down the Labour Government and force a general election, with Mrs Thatcher entering Downing Street.
Mr Corbyn shared the video, captioned “Forty years ago today, @theSNP did this...”
It contains footage of SNP MP Tommy Sheppard’s comments from last year that “in retrospect, I would have done exactly the same thing”.
Following Mr Corbyn’s tweet, SNP leader Nicola Sturgeon replied: “Dear @jeremycorbyn - instead of talking about things that happened when I was eight years old, how about showing some leadership today?
“You could start by asking yourself why the polls show you still trailing behind the most incompetent Tory government in our lifetimes.”
Mr Sheppard added: “The clip they’re showing from me in the House of Commons says that I understand why people voted to have an election in May 1979 and I would probably have done the same thing.
“But Labour are trying to imply that I said I would support the election of the Thatcher government. This is a first order lie. I have never voted Tory in my life.
“The SNP have consistently opposed the Tories unlike Labour who worked hand in glove with them to prevent people in Scotland taking control of their own affairs.”
SNP MP for Perth and North Perthshire, Pete Wishart, noted he was still a teenager at the time of the no-confidence vote and said: “A time of national crisis and the leader of the Labour Party tweets a nonsensical interpretation of events from 1979.”
Stewart McDonald, the SNP MP for Glasgow South, added: “How about you get off your arse and deal with the problems we face right now rather than indulging yourself in more fantasy bogeyman trash?”
The vote on no confidence followed the industrial unrest known as the Winter of Discontent and the referendum on the Scotland Act for greater devolution which, despite winning a majority, was not passed due to turnout not reaching the 40% threshold.
In the debate about the vote, Mr Callaghan said: “Tonight, the Conservative Party, which wants the act repealed and opposes even devolution, will march through the lobby with the SNP, which wants independence for Scotland, and with the Liberals, who want to keep the act.
“What a massive display of unsullied principle. The minority parties have walked into a trap.
“If they win, there will be a general election. I am told that the current joke going around the House is that it is the first time in recorded history that turkeys have been known to vote for an early Christmas.”