It finished Kilkenny 3-22 Galway 5-16.
The Cats led by 9 points with four minutes to go.
But a hat-trick of goals in the last few minutes- two from Conor Cooney and another from Joe Canning from the penalty spot, levelled the game.
Substitute Henry Shefflin then looked to have won the game for Kilkenny with a point from a tight angle.
But Canning scored the equaliser from out on the touchline deep into injury time to draw the match.
The replay will take place next Saturday, with the winners set to face Dublin in the Leinster final in a fortnight.
Elsewhere, Kerry will face Cork in the Munster Football Final, after they beat Clare by 1-17 to 1-13 in Ennis.
And Donegal are into a fourth straight Ulster Football Final, after a 3-16 to 0-12 win over Antrim in Clones.
