Mendes, 16, had stunned the world No 1 by going 2-0 up in the first leg, but after a late formation tweak, Liverpool's Hunt struck back with two stoppage-time strikes to grab a 2-2 draw.
In his sixth consecutive tournament final, Hunt pressed his opponent in the second leg, before Eden Hazard put Liverpool 3-2 up on aggregate.
But Mendes did not relent as a goal from Son Heung-min forced extra-time.
The final looked all set for penalties before Dominic Calvert-Lewin's towering header in the second minute of added time won it for Hunt.
It set up a Grand Final against PlayStation champion Kyle Leese (KyleLeese_), of Manchester United.
"That's the craziest game I've ever played in," Hunt said. "I started really slow in the first leg, but got two goals late.
"Even when I'm 4-0 up I'm still nervous, so imagine when it's so tight, it's so scary ...
"Here we are again, Grand Final. Like I say, anyone but United, so let's go."