Mourinho's charges twice came from behind in the Greek capital as captain Fede Valverde came off the bench to rocket home a spectacular winner.
Los Blancos and PSG are the only two sides to win all four of their games so far in the league phase and Mourinho only trails the defending champions on goal difference at the top of the rankings.
Kylian Mbappe bagged his fourth European goal of the campaign, as Real Madrid's second equaliser of the night, and the Frenchman moves onto 16 goals so far in 2026/27.
He remains fifth on the Champions League all-time scorer list, now on 74, plus 26 assists.
A 100 goal involvements in 102 games is an incredible benchmark for Mbappe, but he narrowly missed out on breaking Lionel Messi's spectacular record, after the Argentinian managed it in 101 appearances at Barcelona.