Spain had never beaten France in a major tournament yet Alonso's thumping header after 19 minutes and a penalty in second-half injury time were enough to end that run and eliminate a France side who were punished for adopting a lamentably negative approach at the Donbass Arena.
The reigning champions were hardly impressive either, creating few real chances having set up in a 4-6-0 formation, yet their suffocating passing game delivered a 2-0 victory, with France's abject performance raising real questions for coach Laurent Blanc, who had surrendered the initiative from the very first minute.
By contrast, Vicente del Bosque was left to contemplate a semi-final meeting with Portugal and Cristiano Ronaldo as Spain's attempt to surpass the achievements of France and West Germany before them and win three major tournaments in succession continues.
Spain's reputation preceded them prior to kick-off as fearful France coach Blanc deployed his side in an overtly defensive formation, Anthony Reveillere coming into defence as Mathieu Debuchy was pushed forward in order to try and suppress Andres Iniesta. Surprisingly, Samir Nasri was also dropped, the usual Blanc favourite being replaced by Florent Malouda who dropped deeper in midfield in an understandable attempt to deny the reigning champions space in front of goal.
Del Bosque, meanwhile, opted to revert to the striker-less formation that brought Spain a 1-1 draw against Italy in their opening game as Cesc Fabregas replaced Fernando Torres and adopted the false nine position, meaning at kick-off there was only one striker on the pitch: Karim Benzema, who had the unwanted record of having 17 shots without success at the finals.
France's conservatism contributed to a rather sterile first half in Donetsk that was only briefly punctuated by genuine goalmouth action.
The Spanish were quickly into their passing rhythm, France's deep deployment allowing them to dictate the flow of the game and spread the ball across the width of the pitch. Meanwhile, Blanc's side merely sat back and invited pressure in an inhibited performance.
That allowed Spain to play the game their way, an opportunity Alonso grasped with both hands as he tried to score a trademark long-range effort after only eight minutes, only to see Hugo Lloris catch his shot as it threatened to float over his head from all of 45 yards.
Just 11 minutes later Alonso did mark his 100th cap with a goal - and it came via rather more unconventional means for the midfielder. France's strategy to field two right-backs unravelled as Iniesta slipped a neat pass into the left channel for Jordi Alba, who exploited a slip from Debuchy to pick out Alonso with a cross to the back post. Completely unmarked, the Real Madrid star powered a header back across goal and past Lloris.
Conceding early posed a problem for France, whose whole approach was based around containment. Their response was so remain cautious though and they threatened only intermittently, Benzema thumping one free-kick high into the stands before Yohan Cabaye went much closer with a set-piece of his own that forced Iker Casillas into a smart save.
Spain had all the initiative, and predictably dominated possession, yet they found good chances to be elusive. Fabregas was combining well with the midfielders behind him - one clever one-two with Iniesta resulting in the latter having a shot deflected wide - yet a lack of a presence in the centre of the box meant Del Bosque's side were not as penetrative as perhaps they should have been and Spain had to make do with a one-goal advantage at half-time.
France initially improved in the second half, showing more intent and bringing more energy to their performance, but still Casillas was untested as Debuchy headed over from 10 yards out when getting on the end of a cross from Ribery.
After Lloris had made a fine save when racing off his line and preventing Fabregas from getting on the end of a lovely Xavi through-ball and dancing round him, Blanc took action when bringing on Nasri and Menez for Debuchy and Malouda.
Menez soon made himself busy and on 72 minutes almost had a sniff at goal. Yann M'Vila released Ribery with a beautiful pass and after the midfielder pulled the ball back from the byline, only the extended arm of Casillas prevented Menez from connecting. However, the PSG star then let himself down when being booked for dissent and incurring a one-match suspension in the process.
The ball remained Spain's possession for large swathes of the second half but they did precious little with it. Indeed, as France began to probe with more intent - throwing on striker Olivier Giroud for M'Vila with 10 minutes remaining - suddenly Spain looked potentially vulnerable.
However, the threat from France never materialised. Instead it was Spain who pushed for a second goal and their chance arrived in injury time. Substitute Santi Cazorla played in Pedro in the box and the Barcelona forward drew a clumsy challenge from Reveillere with a clever stepover and change of direction.
Alonso sent Lloris the wrong way from 12 yards to take Spain forward to the final four, with France meekly taking their leave of a tournament they never really threatened to leave their mark on.