Real Madrid eased to a relatively comfortable 2-0 derby victory over Rayo Vallecano despite playing over 70 minutes with a man less following Sergio Ramos' dismissal.
In Jose Mourinho's 100th league game in charge, Real took the lead after just three minutes when Morata, on his first league start, slotted home at the far post following a low ball from Mesut Ozil across the six-yard box.
Ozil was again involved as Real made it 2-0 in the 12th minute, the Germany international sending in a free-kick from the right which Ramos headed home after holding off his marker.
But Ramos was dismissed on 18 minutes when, after picking up his first yellow card after brushing Roberto Trashorras off the ball, he was shown red after a Jose Manuel Casado cross hit his hand at close range.
Diego Costa repaid the faith of his coach as he found the target on his return to the side in Atletico Madrid's morale-boosting 3-0 victory at Real Valladolid.
Atletico wasted little time in taking the lead, just 10 minutes on the clock when Radamel Falcao netted his 23rd of the season, although the Colombian was lucky to be given the benefit of the doubt in a close offside call.
Costa made it two just eight minutes into the second half after he was played in by Jorge Koke's cute header and he finished low and hard beyond the goalkeeper.
The visitors' victory was cemented in the final minute as a defensive blunder allowed Cristian Rodriguez to add a third, the substitute gleefully poking the ball home from close range after Antonio Rukavina's attempted chest back to his goalkeeper fell short.
Ten-man Valencia claimed an unlikely 2-0 win to add to struggling Real Mallorca's relegation worries in the Primera Division.
Things looked to be going wrong for the hosts when a slow start was compounded by having midfielder Tino Costa sent off in the 28th minute for a bad foul on Jose Nunes.
But Mallorca could not take advantage and went behind in the 59th minute when Ricardo Costa headed Valencia in front before Roberto Soldado doubled the lead in the 81st minute with a low finish.
Real Sociedad missed a chance to gain ground in their bid to qualify for the Europa League after being held to a 1-1 draw at home by Levante.
Carlos Vela put the hosts in front on 17 minutes from the penalty spot after the Mexico international had been brought down by Nikos Karabelas.
Ten minutes later Levante were given a penalty of their own, when right-back Christian Lell was pushed over in the box by Chory Castro, and Michel converted from the spot.
Michel struck the bar shortly after half-time before Karabelas was shown a second yellow card of the game on 56 minutes, which made it the eighth game in a row in which Sociedad's opponents had had a man sent off.
Espanyol's remarkable revival under coach Javier Aguirre continued as a solitary Sergio Garcia goal secured a 1-0 home win over Real Betis.
Christian Stuani struck a post early on for Espanyol before he created the only goal on seven minutes when the Uruguayan surged down the right wing to pick out Garcia, who steered his shot beyond Adrian.