Portugal's Cristiano Ronaldo and Nani will surely give Spain more to think about than a limp France did in a match which, despite being between two of the powerhouses of European football, produced little incident or excitement.
Spain again played without a recognised striker with Fernando Torres left on the bench, and their patient 'Tiki Taka' football at times became little more than negative possession designed to cajole the French into opening up.
At the other end, Spain goalkeeper Iker Casillas had just one attempt on goal to save as the world champions completed their eighth successive knockout game in a major tournament without conceding a goal.
"It is very difficult to create danger for them, they are so tough to beat, you have to be very clinical when you only get 30-35 percent of the possession," said France coach Laurent Blanc.
The win was the first for Spain in a competitive match against France at the seventh attempt and avenged their loss in the second round of the 2006 World Cup.
Alonso gave Spain the lead in the 19th minute with a powerful header and made sure of the win with a stoppage-time penalty. In between, the world champions were content to keep the ball, often with little attacking purpose.
"We controlled the match well from start to finish and Iker hardly had a save to make. The important thing now is that we recuperate for the next game," said Spain coach Vicente del Bosque.
France came into this tournament having apparently resolved the internal disputes which wrecked their 2010 World Cup campaign but they leave with just a solitary win over Ukraine and they bowed out with a strange lack of determination.
Blanc set up his team in a defensive fashion, bolstering the right flank to try to contain Andres Iniesta.
Right back Mathieu Debuchy was moved forward into midfield ahead of full-back Anthony Reveillere and the defensive-minded Florent Malouda started in midfield in preference to Samir Nasri and Alou Diarra.
It was a logical, if negative, approach for Blanc to take but it was only going to work if the French succeeded in frustrating Spain for a long stretch.
Instead, however, Spain got ahead in the 19th minute and exactly from the side which Blanc had tried to lock down.
"We had analysed the Spanish line-up well because they had two very strong players on the left but what is the most frustrating thing is that we conceded the goal from that side," said Blanc.
Iniesta fed the overlapping Jordi Alba who got to the line and put in a deep cross which Alonso met with a powerful downward header.
France needed to find an attacking response but they went in at half-time having managed only a curling free-kick from Yohan Cabaye which Casillas pushed around the post.
After the break, Franck Ribery did well to create space for a rare cross which Debuchy headed over but with no sign of change to the rather weary pattern of the game, Blanc brought on Nasri and Jeremy Menez just after the hour.
The expected creativity and urgency never really arrived, however, and a spiritless exit for the French was confirmed when in stoppage time Spain substitute Pedro was tripped by Reveillere and Alonso confidently converted the spot-kick.
Spain now have an all-Iberian clash to look forward to back in Donetsk where the fans can at least expect Portugal's aggressive counter-attacking style to provide some moments to raise them from their seats.
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