The decisive moment arrived deep into added time when Nobel Mendy fouled Brahim Diaz inside the penalty area in the 100th minute. Mbappe stepped up and calmly sent his spot kick home, lifting Real to within one point of the league leaders and sparking celebrations among a crowd that had grown increasingly tense as the game unfolded.
Real had made a bright start but were dealt a major blow after just 10 minutes when Bellingham pulled up clutching the back of his left thigh. The England midfielder was visibly upset as he left the pitch, though he was later seen walking without assistance, offering some reassurance to the home support.
Shortly after Bellingham's exit, Vinicius Jr gave Real the lead with a superb finish, cutting in from the left before curling the ball beyond the goalkeeper. Rayo, however, refused to wilt and gradually grew into the game, with Pep Chavarria firing over shortly before the interval as the visitors sensed an opportunity.
That belief was rewarded just after the restart when Jorge de Frutos drew Vallecano level. He reacted quickest to a knock-down from Alvaro Garcia and swept a first-time effort past Thibaut Courtois, who later had to be alert to deny Andrei Ratiu with a smart save using his feet.
Real pushed hard to regain control and came close on several occasions. Mbappe rounded goalkeeper Augusto Batalla after he had strayed outside his area, only to see his shot strike the crossbar. Eduardo Camavinga then went even closer, his header crashing against the post as frustration mounted.
Vallecano's resistance was weakened when Pathe Cisse was shown a straight red card with 10 minutes remaining for a reckless challenge on Dani Ceballos. Even so, the visitors continued to battle, prompting whistles of anxiety from the stands as time ticked away.
Relief finally arrived when Mendy's late challenge on Diaz handed Real a penalty, which Mbappe dispatched for his 22nd league goal of the season. There was still time for more drama as Chavarria received a second yellow card for a push on Rodrygo in the 103rd minute.
The victory marked Real Madrid's sixth consecutive league win, while Rayo Vallecano remained precariously close to the relegation zone, just one point above the bottom three.
