Zinedine Zidane’s men appeared to be on their way to their third league draw at the Santiago Bernabeu in succession – something that last happened in 1969-70 – but Morata found the net with seven minutes left on the clock to help his side to victory.
Comfortable wins over Real Betis and Legia Warsaw suggested Madrid were on the right path again after four games without a win preceding those two results, yet Athletic caused them all kinds of trouble at the Bernabeu.
Things looked positive for Madrid early on, with Karim Benzema opening the scoring after just seven minutes to set them on their way, only for Sabin to restore parity in the 27th minute.
Madrid created plenty of chances to regain the lead, with Cristiano Ronaldo in particular rather wasteful in front of goal, and they eventually scored the crucial second in the closing stages via Morata.
Madrid sit top of the table following this weekend’s results with 21 points from nine games, one clear of second-placed Sevilla, with Barcelona in third on 19 points.
Athletic made an encouraging start to the game and threatened via Mikel Rico and Inaki Williams in the opening exchanges, but it was the hosts who grabbed the lead.
Isco collected a pass from Marcelo, shrugged off Enric Saborit and squared the ball for Benzema, who slotted home through the legs of goalkeeper Gorka Iraizoz for his fourth goal of the season.
The Bernabeu side immediately went in search of a second goal and Toni Kroos, Gareth Bale and Ronaldo all came close to extending their lead, only for Athletic to then restore parity from out of nowhere.
Pepe failed to cope with the physicality of Javier Eraso after a cross from the right, with the ball eventually somewhat fortunately falling to Sabin, who volleyed past Keylor Navas from close range.
Ronaldo should have restored Madrid’s lead in the closing stages of the first half, but his finishing let him down twice. He first failed to get his foot to a cross from Bale after the Welshman’s superb run down the left, before wasting an even bigger opportunity after a quick counter-attack, his weak attempt barely troubling Iraizoz.
Williams should perhaps have given the away side the lead early in the second half when he aimed a shot over the crossbar from the edge of the box after more poor defending from Pepe.
It was not Ronaldo’s night as the Portugal international missed another chance to restore his side’s lead when he volleyed high and wide after a cross from the left, before sending a tame header wide of the target after Kroos’ free-kick.
Mateo Kovacic and Bale were then both unfortunate not to add their name to the scoresheet, before Morata eventually popped up to make the difference. The former Juventus striker had his initial attempt save by Iraizoz, but he was quick to tap home the rebound.
Madrid escaped a second equaliser shortly afterwards when Williams failed to find the net following an error from Raphael Varane, Navas managing to palm away his chipped effort.
Ronaldo could have netted a third for Madrid well into stoppage time, only to be denied by Iraizoz again on what was a frustrating evening for the attacker but an ultimately successful one for his team.