The visitors had the game’s first attempt in the fifth minute when Arnau Martínez did well to work Thibaut Courtois from a tight angle, but Real immediately showed their own threat with Paulo Gazzaniga being called into action by Kylian Mbappe mere seconds later.
Beautiful link-up play on the quarter-hour mark culminated in Vinicius Junior heading over the crossbar, and there was further disappointment for the Brazilian when he was halted by Daley Blind at the end of a blistering break.
Being met by a resolute Girona defence, Real Madrid remained patient with their play and Brahim Díaz’s venomous strike was palmed away by Gazzaniga before Modric fired over.
Los Blanquivermells also got forward when they could and Donny van de Beek caused a scare, although there was another rapid break that required a superb intervention from Ladislav Krejci to prevent Vinicius’ pass from reaching Mbappe.
Modric then provided a moment of pure magic to find an opener before the break, chesting down David Lopez’s attempted clearance and effortlessly sending a sensational strike into the top corner.
Gazzaniga denied Mbappe again and Krejci did enough to stop Rodrygo’s header, but a Real Madrid second finally arrived in the 83rd minute.
Vinicius linked up with Mbappe and poked the ball past Gazzaniga, making sure that Los Blancos ended their three-game winless run in La Liga - they now only sit behind league leaders Barcelona on goal difference.
The hosts also inflicted the seventh defeat from Girona’s last eight matches across all competitions.