The loss of Ed Miliband's frontbench star has been compared to Michael Portillo's defeat in 1997, which has become infamous in modern British political history as a marker for unexpected losses.
Ms Black will become the youngest MP since 13-year-old Christopher Monckton won in 1667 when she takes her seat at Westminster later this month.
However her victory celebrations are likely to be cut short by the need to complete her final year politics exams at Glasgow University.
"The people of Scotland are speaking and its time for their voice to be heard at Westminster," Ms Black said after her shock victory.
She managed to turn a 16,614 Labour majority into a 5,684-vote victory thanks to a swing in the vote towards the SNP of 26.9 per cent.
Speaking immediately after the result was declared, Mr Alexander said: "This of course has been a very difficult night for Labour.
"Scotland has chosen to oppose this Conservative government, but not place that trust in the Labour party. It will be our responsibility to re-win that trust in the months and years ahead."
Alex Salmond, the former SNP leader, cut off from a broadcast interview at the count in Gordon to watch live as Mr Alexander - a key figure in the No campaign against Scottish independence last year - was defeated on live television.
The former first minister of Scotland rose to his feet and muttered "she's a star" as the young candidate delivered her victory speech.
Ms Black has faced criticism during this campaign for tweeting about her boozy nights out on Smirnoff Ice and posting a message that read: "I really f***** hate Celtic."
Yet even on the eve of the poll Scottish Labour figures were insisting that Mr Alexander would see off Ms Black thanks to his local reputation.
The result leaves Mr Alexander, Labour's general election campaign chief, without a seat and fighting to keep his political career afloat.
