Ms Harman said she did not report the "horrible" incident at the time, but rejected the advances from Prof TV Sathyamurthy, who has since died.
His widow has called the allegation - made in the MP's forthcoming memoir - "very dubious" and "hard to believe".
The University of York has called the claims "extremely concerning".
Speaking to the BBC's Andrew Marr, Ms Harman recalled how she had been invited to a meeting with her university tutor, who told her she was "borderline" between a 2:1 and 2:2 grade.
She claimed the tutor told her: "It will be a 2.2 unless you have sex with me."
Asked why she did not report him, she replied: "I thought nobody would listen, that he would deny it and that they would take his side. He was in a position of authority."
"A man in a position of authority that can actually shape your future life can abuse their power for sex," she added.
Prof Sathyamurthy died in 1998, but his ex-wife, Carole Satyamurti, 77, told the Daily Mail: "That's horrible. I find this very hard to believe. The story sounds very dubious to me.
"He was very brilliant and full of jokes, but very respectful of women. I'm sure he wouldn't have done that."
But Ms Harman told the BBC: "The idea that I would invent it - why would I?
"I've said it happened now, having not said anything about it before, because I think we need to look at how we make sure those people who are put in that position, feel able to complain, and those who do that, are held to account."
Ms Harman, who graduated in 1972 aged 21, said she still gained a 2:1 in politics, despite rejecting his advance.
York University's registrar and secretary, Dr David Duncan, said the university strongly condemned all forms of sexual harassment.
"The allegations made by Ms Harman are extremely concerning," he said.
"Behaviour of the sort described by Ms Harman would constitute gross misconduct and would lead to dismissal."
Labour's former deputy leader Harriet Harman has claimed she was offered a better grade in exchange for sex while studying for a politics degree.