An excellent second half strike from Jack Grealish cancelled out Leandro Trossard's well taken goal on 37 minutes.
Brighton were the better team in the first half but the match turned into a scrappy affair after the break.
At the final whistle Maupay had an angry confrontation with his former Brentford teammate Ezri Konsa.
Players from both teams piled in, including Aston Villa assistant John Terry, to separate the feuding duo. It ended with Albion skipper Lewis Dunk dragging Maupay away and down the tunnel.
The draw leaves Albion 14th in the Premier League table just three above the relegation zone. Villa remain third from bottom.