The Republic of Ireland international has been eased into Manuel Pellegrini's team following his August move from Dutch side AZ Alkmaar and Cucho Hernandez was preferred from the start against Los Blancos.
However, Pellegrini threw Parrott on after 68 minutes in place of Hernandez, and the Dubliner seized his chance in the closing stages to slot past Thibaut Courtois from close range.
A 1-0 victory makes it three wins from four games so far in 2026/27 for Pellegrini, with Real Madrid's 100% record ended under Jose Mourinho, and Parrott was delighted at full-time.
"It was a crazy game for my home debut. I think it was a good watch for everybody.
"The fans were amazing tonight. Th way they cheered for the whole game was beautiful.
"I feel amazing. To score a goal against a big team, like Real Madrid, it's a great night."