Christodoulopoulos stood over the free-kick from around 35 yards out with AEK 2-1 down against their rivals and only 11 minutes left.
But, seemingly unfazed by the challenge ahead, he unleashed his strike into the top corner and left Olympiakos goalkeeper Stefanos Kapino rooted to the spot.
Midway through its flight, the ball completely switched direction and crashed into the net, deceiving Kapino.
Christodoulopoulos's superb strike shifted the tone of the match as AEK went on to secure a dramatic 3-2 victory thanks to Petros Mandalos's 89th minute winner. There was still time for both sides to have a man sent off after that too.
Athens top the Greek Super League with four wins and a draw from their opening five matches, five points ahead of Olympiakos – champions for seven years running.
