Sevilla drew level on points with Barcelona at the top of La Liga when they snatched a 2-1 comeback victory at home to Villarreal, while champions Atletico Madrid won 1-0 in a bad-tempered clash at Getafe on Sunday.
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.
Coach Diego Simeone goes home 'content' after his team's 1-0 loss in their Champions League match on Wednesday
A lacklustre Barcelona squandered the chance to go top of La Liga after crashing to a shock 1-0 home defeat by Malaga on Saturday.
Barcelona have been boosted by the successful return from injury of talismanic playmaker Andres Iniesta as they prepare to host city rivals Espanyol in La Liga on Sunday.
News of all that's transpired on and off the football field
Atletico Madrid knocked Barcelona off the top of La Liga, for a day at least, as a second-half strike by Koke earned a 1-0 victory over a stubborn Malaga side on Saturday.
Luis Suarez is starting to "feel like a footballer" once again after being allowed to train with new club Barcelona following his appeal against a FIFA ban for biting an opponent at the World Cup.
Antoine Griezmann headed two goals for Atletico Madrid in a 3-1 victory over Levante that kept them on the heels of La Liga leaders Real Madrid on Saturday.
Atletico Madrid's Jackson Martinez scored his first goal for the club when he came off the bench and curled in a superb effort to seal a hard-fought 3-0 victory at Sevilla in La Liga on Sunday.
Atletico Madrid kept pace with leaders Barcelona and restored their five-point lead over third-placed city rivals Real when Diego Costa and David Villa each scored a penalty in a 2-1 win at Granada in La Liga on Thursday.
Andy Murray clinched the Vienna Open title on Sunday with a 5-7, 6-2, 7-5 victory over David Ferrer, one of the Briton's main rivals in the battle to qualify for the ATP World Tour Finals.
With the distraction of two individual scoring records safely out of the way, Barcelona forward Lionel Messi can turn his full focus on helping the club win the major silverware that eluded them last season.
A late double from Cristiano Ronaldo put some gloss on a stuttering performance from Real Madrid as they beat Celta Vigo 3-0 to cut the gap at the top of La Liga to five points.
Fernando Torres stole the show with a dramatic double as Atletico Madrid secured a battling 2-2 draw at Real Madrid on Thursday that dumped the holders out of the King's Cup 4-2 on aggregate.
Espanyol's Felipe Caicedo came off the bench and netted two late goals to secure a 2-0 win at home to 10-man Valencia on Tuesday that sent the Barcelona-based club through to the King's Cup quarter-finals 3-2 on aggregate.
A subdued Fernando Torres helped Atletico Madrid to a 2-0 win over local rivals Real in the first leg of their King's Cup last-16 tie on Wednesday in his first start since his return to his boyhood club.
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.
Barcelona eased into the King's Cup last 16 when goals from Pedro, Cristian Tello and Neymar secured a 3-0 second-leg victory at home to third-tier Cartagena on Tuesday for a 7-1 aggregate success.
Real Madrid took full advantage of Barcelona's shock defeat at Real Valladolid with a 3-0 home win over 10-man Levante on Sunday that put Carlo Ancelotti's in-form side three points clear at the top of La Liga.
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.
Antoine Griezmann and Yannick Carrasco each conjured moments of magic as Atletico Madrid recaptured top spot in La Liga from Barcelona with a hard-fought 2-0 victory at Celta Vigo on Sunday.
Real Madrid closed to within two points of La Liga leaders Barcelona after demolishing nine-man Rayo Vallecano 10-2 while Atletico Madrid missed a chance to seize top spot outright by losing 1-0 at Malaga.
'I feel as confident and motivated as at the beginning. I can't control rumours, but I still have faith'
Atletico Madrid took advantage of Barcelona's slip-up to go top of La Liga with a 4-0 victory over Real Sociedad as Real Madrid drew 1-1 at Athletic Bilbao and Cristiano Ronaldo was sent off on Sunday.
In an exciting weekend for football lovers, Cristiano Ronaldo and Lionel Messi continued their extraordinary double act, both scoring hat-tricks as Real Madrid and Barcelona maintained their battle for supremacy at the top of La Liga. Chelsea's unbeaten start to the Premier League season ended with a dramatic 2-1 defeat at Newcastle United on Saturday but no-one can get the better of Bayern Munich, who marched on in the Bundesliga with a 1-0 win over Bayer Leverkusen. We present a summary of events in photos.
A summary of sports events and persons who made news on Saturday
Champions League holders Real Madrid will face former European champions Liverpool, FC Basel and debutants Ludogorets of Bulgaria following the group stage draw on Thursday.
Barcelona lost ground on La Liga leaders Real Madrid when their 11-match winning streak was snapped by Malaga, while Premier League pacesetters Chelsea dropped points at home to Burnley. Bayern Munich enjoyed a second-successive goalrush in the Bundesliga after routing Paderborn 6-0 while AS Roma lost ground to Serie A leaders Juventus after yet another draw. This and more from the happenings in the world of football over the weekend.