His first was a bullet header from a Dani Carvajal cross in the second minute and he scored a second deep in injury time at the end of the game as he took the ball around home goalkeeper Geronimo Rulli and slotted home.

In between, 20-year-old midfielder Marco Asensio scored with a cool finish, lofting the ball over Rulli after a long ball caused confusion in the Real Sociedad defence five minutes before the break.

It may not have been quite as emphatic an opening as Barcelona's 6-2 hammering of Real Betis on Saturday but Real coach Zinedine Zidane will have been encouraged by the display from a depleted team missing, among others, injured superstar striker Cristiano Ronaldo.

Earlier on Sunday, Sporting Gijon began their campaign with a 2-1 victory over Athletic Bilbao at El Molinon.

Croatia striker Duje Cop put Sporting in front in the 50th minute and Victor Rodriguez added a quickfire second three minutes later.

Athletic pulled one back through substitute Borja Viguera with four minutes remaining but Sporting held on.

Atletico Madrid were held to a 1-1 draw by Alaves in extraordinary circumstances at the Vicente Calderon.

Diego Simeone's side had seen their principal title rivals Real and Barcelona claim maximum points and missed a series of chances before Kevin Gameiro took advantage of a debatable penalty award to put the Rojiblancos ahead in the third minute of second-half stoppage time.

However, they let two points slip from their grasp as Manu was allowed the space to unleash a right-foot rocket two minutes later, which Atletico goalkeeper Jan Oblak, who had barely touched the ball owing to Atletico's total dominance, got nowhere near.