Serbian Milos Spasic scored a brace in the 31st and 61st minutes.
Iranian forward Shahab Zahedi halved the deficit in the 78th minute.
Five minutes later, Kisvarda’s player Enec Alic was sent off.
The visitors then equalized through a penalty kick converted by Artem Favorov in the 86th minute.
Kisvarda remained undefeated in its fifth championship in a row, while Puskas Academy has not lost in its third league match in a row.