Los Blancos recorded their 21st win of the season in a hotly-contested capital derby, moving 13 points clear of Pep Guardiola's Barcelona in the process
Rayo pushed hard to find an equalizer and but for a splendid save from Iker Casillas it would have been rewarded for its dogged defensive display. But it wasn't to be as Jose Mourinho's side, who was guilty of spurning numerous chances itself, held on to its slender advantage and move ominously closer to the Primera Division title.
After a competitive start, Los Blancos had the first opening when Gonzalo Higuain latched onto Kaka's chipped pass. The striker struggled to get the ball out from under his feet and despite managing to round the keeper, the angle became too acute as the opportunity disappeared.
The early exchanges were devoid of any clear cut chances, but drama then ensued when Diego Costa was left outraged as Sergio Ramos raised his elbow in the penalty area. The referee remained unmoved, however, and Costa was shown a yellow card for his continued protests.
As the first half drew to a close Michu came within the width of the post from giving his side the lead. The Spaniard brought down a cross field ball before dummying a shot and cutting inside. He then lashed an effort goal wards which rebounded off the angle of the upright and crossbar.
The home side continued to push and Madrid needed Ramos' right foot to save them from falling behind when he touched the ball off of Michu's toe. He was left relieved to see the ball pinball behind for a corner as it remained goalless at the break.
However, Real Madrid has been clinical in producing winning performances this season, and took the lead early in the second half. From a corner, Cristiano Ronaldo chased the ball away from goal before cheekily attempting a backheel which he flashed into the net.
Soon after the opening goal the former Manchester United star tested the hands of Joel with a driven free-kick from 25-yards out which he did well to punch clear. Rayo's stopper was then called upon again when he needed to get to a loose ball ahead of Higuain.
Casillas was then forced into a flying save to maintain the advantage. The Spain No. 1 punched clear a corner kick, inviting Jose Casado to strike from 30 yards out and it was a vicious effort heading into the top corner but for Casillas' hand which tipped the ball around the post.
Jose Callejon then spurned a chance to double Madrid's advantage when he was left unmarked in the six-yard box but failed to direct the ball on target. Joel ensured that a point remained a possibility as the game entered the final stages, pulling off a wonderful stop to deny Ronaldo from grabbing his second of the match with an effort from range.
Any chance of the hosts coming away with a point vanished, though, when Michu was shown a red card late on for a rash challenge. Real Madrid hung on for an invaluable victory in the quest for the title and the importance of the three points was evident by the players reaction at the end of the match.
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