Morata, who had scored his first goal for the club in last week's 2-0 win over Villarreal, rose to head home from close range on the half-hour mark following a corner which had been flicked on by Atleti captain Diego Godin.
The Belgian forward came off the bench to make his Real debut in Saturday's 3-2 win over Levante, having had his start to life at the club hit by a thigh injury the day before the La Liga season began.
News of all that's transpired on and off the football field.
News of all that's transpired on and off the football field.
News of all that's transpired on and off the football field
News of all that's transpired on and off the football field.
Messi stretched Barca's lead by finishing off a brilliant move with Luis Suarez in the 50th minute and the Uruguayan joined his close friend and strike partner on 15 league goals by robbing an Eibar defender and finishing inside the near post in the 68th.
Holders Barcelona produced a second-half blitz to come from behind and beat Athletic Bilbao 3-1 to book a place in the King's Cup semi-finals after Atletico Madrid crashed out in a shock 3-2 defeat by Celta Vigo.
Atletico Madrid maintained a two-point lead in La Liga with a 3-0 victory at Las Palmas and Barcelona and Real Madrid stayed hard on their heels with thumping wins over Athletic Bilbao and Sporting Gijon on Sunday.
United are 16th in the standings with a game in hand heading into the international break.
Lionel Messi will have another chance to match or surpass Telmo Zarra's six-decade-old La Liga scoring record of 251 goals when Barcelona host promoted Eibar on Saturday.
News of all that's transpired on and off the football field
Teenager Curtis Jones grabbed a 58th-minute winner as an injury-hit Liverpool qualified for the knockout stage of the Champions League with a 1-0 win over Ajax Amsterdam at Anfield on Tuesday.
Midfielder Dani Ceballos added: "It looks like us changing our coach worked. We have recovered some sensations we had lost and we have got the three points. Now our objective is to win all the games left and finish the season as well as possible."
Images from the UEFA Champions League matches played on Tuesday.
IMAGES from the soccer matches played in Spain and Italy on Saturday
Atletico Madrid striker Diego Costa haunted Arsenal again by firing his side to a 1-0 win in Thursday's Europa League semi-final second leg to send the Spaniards into the final and deny Arsene Wenger a dream end to his long reign as Arsenal coach.
Real Madrid can bury Atletico's hopes of winning La Liga with a third straight victory against their city neighbours on Sunday that would leave the capital's second club trailing by six points.
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Atletico Madrid's La Liga title challenge took a nosedive when they slumped to a shock 3-0 defeat at Osasuna on Sunday, leaving Real Madrid three points clear at the top.
Lionel Messi overhauled Real Madrid great Alfredo Di Stefano's La Liga goals tally as Barcelona and Atletico Madrid each won on Saturday to pull three points clear of Real at the top.
IMAGES from the La Liga matches played on Tuesday
Atletico Madrid's Brazilian striker Diego Costa scored twice as they came from behind to beat Levante 3-2 at home on Saturday to go three points clear at the top of La Liga.
News of all that's transpired on and off the football field
The result also means second-placed Real Sociedad can reclaim top spot if they beat Eibar on Sunday.
Lionel Messi has been included in Barcelona's squad for Wednesday's Spanish Super Cup second leg at home to Atletico Madrid after recovering from a thigh problem sustained in last week's 1-1 first-leg draw at the Calderon.
Atletico Madrid tore apart city rivals Real Madrid 4-0 at home to open up the La Liga title race on Saturday in a triumph crowned by a spectacular overhead kick goal by Saul Niguez.
Cristiano Ronaldo struck twice as leaders Real Madrid subdued Eibar 4-0 on Saturday while Lionel Messi set a La Liga record of 253 goals with a hat-trick in second-placed Barcelona's 5-1 rout of Sevilla.
A round of Saturday's matches in Series A, La Liga and Bundesliga.
News of all that's transpired on and off the football field
Real Madrid ended their long wait for a La Liga victory by beating Real Valladolid 2-0 on Saturday with two late goals in interim coach Santiago Solari's first home game in charge of the struggling European champions.
News of all that transpired on and off the field.
Atletico Madrid secured a berth in the Champions League group stage for next season and Deportivo La Coruna narrowly escaped relegation when they came from two goals down to draw 2-2 at champions Barcelona on the final day in La Liga on Saturday.
IMAGES from the UEFA Champions League matches played on Tuesday
Neymar scored the opener to continue his rich vein of form as 10-man Barcelona won a one-sided La Liga derby against Espanyol.
Real Madrid's unbeaten start to the La Liga season came to an abrupt and surprising end as Real Mallorca claimed a stunning 1-0 victory at a rocking Son Moix on Saturday to climb out of the relegation zone.
Luis Suarez struck twice and Lionel Messi scored on his 500th appearance for Barcelona who set a new Spanish record of goals in a calendar year with a 4-0 win over Real Betis that lifted them top of La Liga on Wednesday.
Having absorbed the body blow of losing striker Radamel Falcao in the close season, Atletico Madrid have emerged as genuine contenders to break the title stranglehold of Real Madrid and Barcelona.
Griezmann special earns Atletico 1-1 draw at Sevilla
Atletico Madrid demonstrated their remarkable team spirit to come roaring back from two goals and a man down to draw 2-2 at Liga debutants Girona on Saturday, after Antoine Griezmann had been sent off for the first time in his career.
Manchester City boss Pep Guardiola has warned his side to beware of Monaco's "killers in the box" when they host the principality club in the first leg of their Champions League, last 16 tie on Tuesday.
