It was an efficient and calm performance from world champions Spain, who started without a recognised striker before clinching their first competitive win over the French.
But it was a display which left most of the crowd at the Donbass Arena indifferent to its cautious pragmatism.
France coach Laurent Blanc’s tactics of playing two right backs in a defensive lineup failed as Spanish left back Jordi Alba skipped through to the goalline after 19 minutes and picked out an unmarked Alonso who headed firmly home at the far post.
The experienced midfielder coolly converted a penalty in stoppage time to give the defending champions the victory margin their dominance deserved.
France, who had won five and drawn one of the teams’ six previous competitive meetings, were spectators for long spells as Spain played their usual patient possession game without taking any risks.
The only real goal French effort on goal in the first half was a 32nd-minute free kick from Yohan Cabaye which was curling into the top corner before Iker Casillas pushed it around the post.
France livened up after the break with Mathieu Debuchy heading just over after Franck Ribery had wriggled into space for a cross.
Blanc brought on attacking midfielders Samir Nasri and Jeremy Menez just after the hour as he sought a way back into the game but they were unable to make any real impact against a solid Spanish defence.
Alonso added his second goal from the penalty spot in stoppage time after substitute Pedro was tripped by Anthony Reveillere.
Spain are now unbeaten in 18 competitive games since their 1-0 defeat by Switzerland in the group stage of the 2010 World Cup and they have not conceded a goal in their last eight knockout games in tournaments.