The defending champions, who are looking to win a third straight major title, advanced to the European Championship semifinals with a not-so-commanding 2-0 win over France on Saturday. In the next round, Portugal and star player Cristiano Ronaldo could provide a much sterner test.
"These types of games, in this type of competition, are always very tense," Spain coach Vicente del Bosque said of Saturday's win, "and you need to have the know-how to win them."
Alonso provided that.
The Real Madrid midfielder celebrated his 100th international appearance with an early header and a late penalty, a pair of rare goals from a player more accustomed to anchoring the back of the six-man midfield rather than pushing forward with the rest.
"I could never have imagined to reach my 100th cap, to go to the semis and score two goals," Alonso said. "Hopefully the 101st will be better."
Spain's next match will come on Wednesday against Portugal, again at the Donbass Arena in Donetsk. And with Ronaldo improving as the tournament progresses, Spain will likely have to step up a notch to earn a chance to defend its title.
Saturday's opening goal was the result of excellent one-touch football — the hallmark of Spain's game. Andres Iniesta prodded the ball through for Jordi Alba, who whipped a perfect cross from the left. Alonso timed his run so well that no France defender picked him up.
Spain wrapped things up after France right back Anthony Reveillere barged into substitute forward Pedro Rodriguez in injury time. Alonso coolly sent goalkeeper Hugo Lloris the wrong way from the spot, looking right but clipping the ball firmly to the left.
"He knows how to sacrifice himself, help the team and where to play," Del Bosque said of Alonso. "He is one of the attacking strengths of ours. He knows how to create and finish."
The win was Spain's first ever over France in a competitive match in seven attempts. But France wasn't that competitive Saturday, managing only one shot on target.
"When you lose a game there's always something missing, I'm not sure if it's possession or technical ability," France coach Laurent Blanc said. "The lads gave everything and it's very hard to play against Spain. We blocked their left flank, which is their strong point."
France's best moment came in the 32nd minute when Yohan Cabaye's free kick was tipped over by Spain goalkeeper Iker Casillas.
"They were there for the taking," Blanc said. "We knew we would get some chances, and the only thing I regret is that they scored off their first good chance. If we had gone in level at 0-0 at halftime, then I think we would have had more room in the second half."
Although the French made it out of the group stage for the first time since the 2006 World Cup, the manner of Saturday's loss will be disappointing for a team touted as one of the tournament's dangerous outsiders.
France formed a deep defensive line and watched awe-struck as Spain flicked the ball around like a training session. The Spanish made dummy runs everywhere early on, and had a penalty claim waved away in the sixth minute when Cesc Fabregas tumbled under a challenge from left back Gael Clichy.
Fabregas also started against Italy in Spain's opening 1-1 draw, sparking criticism against Del Bosque for not picking a recognized striker. But against France, it worked.
Spain pulled a compact France team out of position in the 10th minute as Iniesta curled a ball behind centre half Adil Rami but it was too far for Fabregas to reach.
Karim Benzema, looking for his first goal at a major tournament, looked sharp and made some good runs, but the Real Madrid striker rarely got any service. He was fouled in the 32nd after running onto Florent Malouda's pass, and Cabaye's free kick was sailing into the top left corner before Casillas shuffled across quickly to save it.
While the French averted a repeat of the 2010 World Cup crisis — when the entire squad went on strike at training — the buildup to Saturday's game was marred by tensions in the camp following a heated dressing room bust-up after the 2-0 loss to Sweden.
"The big teams have all showed up at this Euro, and they will be in the semifinals," Blanc said. "Unfortunately, France won't be."
Spain: Iker Casillas, Alvaro Arbeloa, Gerard Pique, Sergio Ramos, Jordi Alba, Xavi Hernandez, Sergio Busquets, Xabi Alonso, David Silva (Pedro Rodriguez, 65), Andres Iniesta (Santi Cazorla, 84), Cesc Fabregas (Fernando Torres, 67).
France: Hugo Lloris, Anthony Reveillere, Adil Rami, Laurent Koscielny, Gael Clichy, Mathieu Debuchy (Jeremy Menez, 65), Yohan Cabaye, Yann M'Vila (Olivier Giroud, 79), Florent Malouda (Samir Nasri, 65), Franck Ribery, Karim Benzema.