The World Cup winner was dismissed after adding to youngster Alvaro Morata's early opener, but Mourinho's men proved more than capable of coasting to the win.
A thrashing was on the cards for the Rayo as los Blancos raced ahead with goals from Alvaro Morata and Sergio Ramos inside 12 minutes, however, the right back was shown a red card soon after. Although Rayo controlled possession for the remainder of the game, a toothless display in front of goal made it easy for Jose Mourinho's team to close out the win.
Kaka began alongside Mesut Ozil for the home side and the pair combined to create the opening goal with just three minutes on the clock.
The Brazilian played his teammate in on the right side of the area and his cutback was swept in at the far post by Morata, who made his first start of the season.
Los Blancos were in control of proceedings but in the eighth minute Rayo came agonizingly close to an equalizer. Piti spotted Alejandro Dominguez's run through the Madrid defense but the Argentine's cross-goal effort shaded the outside of the post.
Mourinho's side heeded that warning and doubled the lead five minutes later. Ramos, who won a free kick after beating Cassado down the right, got in front of his marker to head home from Ozil's in-swinging delivery.
After a good save from Ruben kept Michael Essien's powerful attempt from distance out, momentum looked to be swinging Rayo's way, even more so when Ramos was sent off having received two yellow cards, the second for handball, in the 18th minute.
Morata was subsequently sacrificed for Raul Albiol as the home side sought to keep a solid shape. Paco Jemez's side thus took charge of the ball, though it was unable to forge any meaningful chances.
Los Merengues were sticking to the counterattack and almost stole a third when Cristiano Ronaldo rounded Ruben but failed to find the back of the net from a tight angle.
Rayo remained in control of possession but was bereft of ideas that could unlock the Madrid defense. The team's impotence nearly saw it fall further behind 10 minutes after the restart but Kaka's rushed shot was screwed wide of the post.
The home side was clearly confident in its ability to close the game out, and it proved to be justified. Alhassane 'Lass' Bangoura looked lively in the wide areas but his side was incapable of getting anyone in behind to test Diego Lopez.
In fact, the team with 10 men was looking more dangerous as Sami Khedira dribbled past the keeper but sent his cutback just out of Kaka's reach.
Victory ensures that Real Madrid keeps pace with Barcelona and Atletico Madrid, which both picked up three points, meaning the gap at the top still stands at 16 points.