Madrid, May 1 (IANS): A Gareth Bale goal 11 minutes from time gave Real Madrid a vital 1-0 win against Real Sociedad to keep his side's hopes of winning the La Liga football title alive.

The Welshman had been guilty of a series of misses in the first half, but his towering leap was enough to separate the two sides in an entertaining game in San Sebastian stadium here on Saturday, reports Xinhua.

Both sides were without key players with Tony Kroos, Ronaldo and Karim Benzema left in Madrid, while the home side had Jonathas, Carlos Vela and Imanol Agirretxe all sidelined.

Real Madrid started the game in control and carved out three clear chances only for James Rodriguez to see his shot parried, before Sergio Ramos glanced a header wide from a corner and Gareth Bale did the same.

The game then opened out and became an end to end with James sending over a fine cross for Bale to head over, before at the other end Xabi Prieto sent a dangerous cross into the Madrid area.

James hit another shot at goalkeeper Geronimo Rulli, before Nacho Fernandez had the best chance of the first half with a run into the home penalty area only to see Markel Bergara clear his shot off the line.

Bale had a wonderful chance to open the scoring shortly before the hour when a mistake from Real Sociedad defender Yuri teed him up eight yards out. Bale hit his shot low only for Rulli to stick out his right foot to make a save.

Jese Rodriguez replaced the ineffective Borja Mayoral with 25 minutes as Real Madrid looked for a goal that would momentarily lift them above Atletico Madrid and Barcelona.

A lovely move involving Bale and Modric ended with Jese's shot parried by Rulli, who then tipped another shot from the substitute wide of the post.

He was helpless 11 minutes from time when Lucas crossed from the right and Bale again outjumped Aritz Elustondo. His header was on target to score a goal which could be worth the league.