By SABC Sport
3rd May 2023
Barca had to overcome stiff resistance from a side reduced to 10 men after Jorge Herrando Oroz was sent off after 26 minutes.
Their patience paid off with five minutes remaining when Robert Lewandowski, who moments earlier had a goal ruled out for offside, crossed into the box.
Frenkie De Jong headed the ball towards Alba, with the Spain international full-back firing home on the volley.
Barca now lead Real Madrid by 14 points with just five matches remaining, after their rivals were beaten 2-0 at Real Sociedad.
Former Real Madrid B forward Takefusa Kubo latched on to Eder Militao's poor pass to open the scoring two minutes after half-time.
The visitors were left a man down on the hour mark when Dani Carvajal was shown a second yellow card for a clumsy foul on Aihen Munoz.
And Ander Barrenetxea, who replaced Kubo in the 74th minute, wrapped up the points when he cut inside and finished past Thibaut Courtois with five minutes remaining.
Elche's relegation was confirmed with a 2-1 defeat at Almeria.
Goals from Leo Baptistao and Adri Embarba, either side of half-time, put the hosts in control before Ezequiel Ponce pulled one back in the closing stages for the league's bottom team.