Academica looked set to add a win to their meagre tally of two points from four games when Schumacher's penalty and Marinho's strike put them 2-0 up in the first half.
But Cape Verdean striker Kuca reduced the deficit before half-time and, after Iago Santos had seen red for the hosts, he netted again 20 minutes from time to ensure the spoils were shared.
The home side took the lead when Emidio Rafael was punished for handling in the area and Schumacher kept his cool from the spot.
Marinho was the beneficiary of some excellent work by Aderlan as the Portuguese tapped home the second from close range.
Kuca began his one-man salvage mission in the final minute of the half with a neat finish from inside the box, and Iago Santos' dismissal for an apparent elbow shifted the momentum further in Estoril's favour.
It was Kuca who drew the scores level with an excellent diving header and substitute Javier Balboa hit the post late on as Estoril finished on top.
