Alba, who set up both of Messi's goals, got on the scoresheet in the 28th minute as Messi repaid the favour to put the win beyond doubt.
Alba was also the provider for the second goal of the game, featuring a lovely one-two that began with a Messi pass and ended with another Messi goal.
With Philippe Coutinho to come into this side, there are no signs of this remarkable campaign losing momentum for Barca. It wasn't until the last minute that Ivan Rakitic netted the fifth from a corner taken by Dembele. Barcelona's all-time scoring leader swept Alba's cross past Sergio Alvarez despite the goalkeeper getting a hand to the ball, and he followed up by firing home after another exchange of passes with Alba.
China's Li Haotong helps Team Asia lead in Eurasia Cup
They dominated throughout the match, with Kang firing birdies on the first two holes, and Poon scoring a birdie on the 14th. Defending champions Europe trail Asia by one point after the opening day of the EurAsia Cup in Malaysia.
With the side of his boot, Alba directed the ideal bouncing ball across the edge of the box for Messi to smash past the goalkeeper with his first touch.
Not long after, Andres Iniesta was also withdrawn from the action, and given there was no need to chase more goals, Barcelona were happy to hold the ball and conserve energy for much of the second period.
Sevilla beat Cadiz 2-1 with goals from Wissam Ben Yedder and Joaquin Correa to advance 4-1 on aggregate.
Thursday's qualifiers join Real Madrid, Atletico Madrid, Leganes, Alaves and Valencia who already sealed their qualification on Tuesday and Wednesday night. "But I shouldn't say that because it will mean we'll draw them!"
Goals by forwards Leo Baptistao and Gerard Moreno helped Espanyol to a 2-0 victory at Levante, sending the Barcelona-based team through 3-2 on aggregate.