Madrid\'s win kept them in third place, four points behind Atletico Madrid after it won 3-0 at Valladolid.
Barcelona: Real Madrid had little trouble hanging on to beat cross-town rival Rayo Vallecano 2-0 despite Sergio Ramos' early sending off, giving coach Jose Mourinho a victory in his 100th Spanish league game on Sunday.
Young striker Alvaro Morata put Madrid ahead in just the third minute. Ramos doubled the advantage with a header in the 12th, but the Spain defender then left the hosts with 10 men in the 18th after picking up two bookings in a two-minute span.
Madrid's win kept them in third place, four points behind Atletico Madrid after it won 3-0 at Valladolid. Barcelona lead Atletico by 12 points at the top of the table with the league almost two-thirds through.
In his third season with Madrid, Mourinho has a league record of 76 victories, 13 draws and 11 losses.
Mourinho marked his milestone by making another change to his starting line up by leaving France striker Karim Benzema on the bench in favour of the 20-year-old Morata.
"We started the match well with two goals in the opening minutes, but then it's always tough to play a man down," Morata said. "I'm playing with some of the best players in the world and learning little by little. I couldn't ask for anything else."
Rayo had earned the label of this season's revelation by not only defying predictions that it would suffer to stay up, but rising into contention for a top-six finish and a European competition berth with their attack-oriented style of play.
However, its fearless approach cost it dearly against Madrid, which has struggled against defensive teams this season while ripping apart sides that dare send too many men forward with its potent counterattack.
Morata grabbed Madrid the lead at the Santiago Bernabeu when he arrived unmarked behind a wave of teammates to drive home a no-look backpass from Mesut Oezil after Kaka had played the Germany midfielder wide on the right flank.
After Rayo forward Alejandro "Chori" Dominguez grazed the upright with a shot, Ramos made it 2-0 after he had earned a free kick just outside the box. He then muscled in front of his marker and turned Oezil's service into the net with a powerfully taken header.
Madrid looked ready to rout Rayo until Ramos saw his two quick yellow cards, the first for fouling Leo Baptistao and the second for blocking a pass with his arm.
"It isn't normal that I'm sent off in two minutes," said Ramos. "I am not one to make harsh tackles with bad intentions. I'm sorry I left my teammates at a disadvantage."
Madrid's top scorer Cristiano Ronaldo, who netted the equalizer against Manchester United in the Champions League on Wednesday, hit the side netting in the 36th in his best chance.
Rayo got a much-needed respite with Ramos' dismissal and managed to take charge of the ball, but it could come no closer to scoring than Roberto Trashorras' try inside the box that he sailed over the bar just before halftime.
Also Sunday, Valencia scored twice after going down to 10 men to beat struggling Mallorca 2-0 at home thanks to goals from Ricardo Costa and Roberto Soldado following Tino Costa's red card for hitting Mallorca's Tomas Pina in the 28th.
Valencia's win lifted it into fifth place, two points from the Champion League positions.
Real Sociedad was held to a 1-1 draw at home by Levante despite having an extra player for the last half hour. Sociedad moved into sixth place after losing just once in the last 14 rounds. Levante stayed in ninth.
Espanyol got its fifth straight home win under new coach Javier Aguirre by downing Real Betis 1-0 from Sergio Garcia's first-half goal as it rose into 12th place.
Atletico bounced back from its first home loss in 20 games against Rubin Kazan in the Europa League on Thursday with its most convincing road performance in league play since September.
"This was one of our best games of the season," said Atletico coach Diego Simeone. "Normally there is stage of the game when the rival responds and the result is put in doubt, but that never happened. We were the better side throughout."
Radamel Falcao scored his 20th league goal this season in the 11th to set Atletico on its way to its first victory in six league matches away from home.
Diego Costa doubled the advantage in the 53rd, and Cristian Rodriguez added a third goal for Atletico in the 90th.