Georgia took a shock lead in the 18th minute of the match, with Robin Le Normand turning a low cross from Otar Kakabadze into the back of his own net from close range, and Willy Sagnol's side were dreaming of another famous win after their success over Portugal last time out.
However, Spain levelled the scores shortly before the break courtesy of a brilliant strike from Rodri, before Fabian Ruiz headed an excellent Lamine Yamal cross into the back of the net to make it 2-1 to La Roja in the 51st minute.
A third then arrived for Luis de la Fuente's side in the 75th minute through Nico Williams, before Dani Olmo scored a late fourth, and Spain will tackle tournament hosts Germany in the last eight of the competition on Friday evening, with the winner of that mouthwatering fixture progressing to the final four.
Spain were not placed among the pre-tournament favourites, but the three-time European champions have now won all four of their fixtures at Euro 2024 and will be confident heading into their clash with the hosts.
Yamal, Williams star for Spain once again
In Yamal and Williams, Spain have two of the outstanding young wingers in European football, and the pair were once again in sensational form on Sunday night.
Yamal set up Ruiz for Spain's second of the match, before Williams netted his side's third late on, and Germany will not relish coming up against the in-form duo in the quarter-finals of the competition.
In truth, it was a dominant performance from De la Fuente's side, who certainly look capable of triumphing at this summer's tournament.
Spain were impressive early on, and the first half-chance came for Pedri in the fifth minute, but the Barcelona midfielder's effort was kept out by Georgia goalkeeper Giorgi Mamardashvili.
Georgia made the breakthrough
Five minutes later, Mamardashvili was again called into action to keep out a header from Dani Carvajal, and some of the football from De la Fuente's side in the early exchanges was a joy to watch.
However, Georgia, firmly against the run of play, took the lead in the 18th minute, as central defender Le Normand, under pressure from Khvicha Kvaratskhelia, turned a cross from Kakabadze into the back of his own net to spark jubilant scenes from the Georgia supporters.
Pedri and Laporte both fired efforts over the crossbar before Mamardashvili denied Marc Cucurella, as Spain looked to respond, but the counter-attack remained on for Georgia, with Kvaratskhelia's pace a real problem for La Roja.
The leveller for Spain finally came in the 39th minute, as the brilliant Rodri picked out the bottom corner with a wonderful strike from just outside the penalty box, and in truth, it was no more than La Roja deserved.
The Spain fightback was so impressive
Kvaratskhelia almost scored a spectacular second for Georgia early in the second period, but his long-range effort, which had Spain goalkeeper Unai Simon scrambling, dropped just wide of the post.
Mamardashvili then kept out a curling free kick from Yamal, but Spain managed to score a second in the 51st minute, with Ruiz heading a brilliant cross from Barcelona's 16-year-old superstar into the back of the net from close range.
Georgiy Tsitaishvili had a chance to level the scores for Georgia in the 68th minute, but his effort from a dangerous position was wide of the post, before Giorgi Gvelesiani turned a Yamal cross into the back of his own net, only for the offside flag to come to Georgia's rescue.
Spain secured their spot in the last eight in the 75th minute, though, with Williams brilliantly picking out the back of the net with a thumping effort from inside the box, before Olmo's clever finish made it 4-1 in the 83rd minute, with the goal capping off an excellent La Roja performance.
What next for Spain and Georgia?
Spain will march onto the quarter-finals, with Germany their opponents on Friday night.
As for Georgia, they can take plenty from their display this summer, and the national side will be back in competitive action against Czech Republic in the UEFA Nations League on September 7.