However Spain’s joy was overshadowed by injuries suffered by David Silva and Alvaro Morata, while Gerard Pique was once again jeered by the home support.
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Cazorla hit the bar on 21 minutes before Spain were forced into another change when Morata was stretchered off, holding his head in despair as he exited.
Spain’s injury list may be growing but at least they have confirmed their place in France, sealing top place in Group C, and they will now have an opportunity to win their third consecutive European Championships.
The Celta Vigo forward’s pass freed Alba inside the area and his cut-back was tapped into an empty net by Alcacer for his sixth worldwide goal in nine appearances.
Spain played with a depleted squad because of injuries and suspensions.
Continental champions for the first time in 1964, they are unbeaten in 32 home qualifiers, winning their last 17 in the Euros since a 1-0 loss to Greece in Zaragoza in June 2003.
A final score of 3-0 would have been a fair reflection of the events, but Cazorla, who was impressive on the night, scored his second in the final five minutes.
Nonetheless, Spain did not lose any focus and continued to rain shots at Sebastien Joubert’s goal, and they were eventually rewarded for their resolve as Cazorla mopped up Pedro’s rebound shortly before the interval.
Cazorla then finished off the rout with only five minutes remaining, the Arsenal midfielder receiving the ball just outside the visitors’ box and proceeding to smash a shot low and hard into the bottom-left corner. A four-goal separation might be a touch harsh, but Spain certainly deserved to emerge victorious. It was not exactly a performance that would have anxious the likes of Germany and France ahead of Euro 2016, but Spain have now not conceded a single goal in a competitive match since last October.
The away side put so much into the first half, however, that the second was always going to be hard.
Vicente del Bosque’s side will be heavy favourites to win against the European minnows in the Group C qualifier at Las Gaunas in Logrono.
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Santi Cazorla (Spain) – Broke the deadlock and was the only player in a Spain shirt who looked motivated throughout.
