Davis took the lead midway through the first half, maintaining his record of scoring in every round with his own character, but Maddison equalised through Jamie Vardy on the stroke of half-time.
The Villa forward again went ahead thanks to his own player, and a Jack Grealish goal put him 3-1 up with nine minutes left.
But Maddison halved the deficit with his own character and then levelled through Wilfred Ndidi in stoppage time. He went on to score a decisive goal with Vardy in the opening four minutes of the golden-goal match.
Day 5 matches
Semi-final: Keinan Davis (AVL) 3-4 James Maddison (LEI)*
Semi-final: Max Aarons (NOR) 1-2 John Egan (SHU) | Report and highlights
Final: John Egan (SHU) 1-5 James Maddison (LEI) | Report and highlights