Willy Sagnol's side took a shock lead in the 18th minute of the contest, with Robin Le Normand turning into the back of his own net from close range, but Spain were level just before the break through Rodri.
Fabian Ruiz, Nico Williams and Dani Olmo then scored in the second period to hand La Roja a 4-1 victory, and they will tackle hosts Germany in the quarter-finals of the competition on Friday.
Here, Sports Mole provides an in-depth analysis of the contest, including highlights, our man of the match and the best statistics from the entertaining contest.
HIGHLIGHTS
5th min: The first half-chance of the match comes for Spain, but Pedri sees his close-range effort kept out by the Georgia goalkeeper.
10th min: Dominant Spain come close again, but Georgia stopper Giorgi Mamardashvili is on hand to keep out a header from Dani Carvajal.
16th min: Spain's third chance comes for Aymeric Laporte, who rises highest to meet a corner from the right, but his effort is wide of the post, with Georgia surviving another dangerous moment.
18th min: GOAL! SPAIN 0-1 GEORGIA (LE NORMAND OWN GOAL)
Georgia, against the run of play, take the lead in the 18th minute of the contest, as Robin Le Normand, under pressure from Khvicha Kvaratskhelia, turns a cross from Otar Kakabadze into the back of his own net.
22nd min: Decent stop from the Georgia goalkeeper once again to keep out a strike from Fabian Ruiz, with Spain looking to respond to the setback.
35th min: Mamardashvili gets down very well to keep out a low drive from Marc Cucurella, with the Valencia goalkeeper called into action once again.
38th min: Another save from the Georgia goalkeeper, this time keeping out Nico Williams.
39th min: GOAL! SPAIN 1-1 GEORGIA (RODRI)
Spain level the scores in the 39th minute, and it is a brilliant goal from Rodri, as the midfielder picks out the bottom corner with an effort from just outside the box.
HALF TIME: SPAIN 1-1 GEORGIA
49th min: Simon scrambles back towards his own goal, as Kvaratskhelia looks to score from distance, but the ball drops just wide of the Spain goal.
51st min: SPAIN 2-1 GEORGIA (RUIZ)
Shortly after a spectacular save from Mamardashvili to keep out a Yamal free kick; the Barcelona youngster turns provider for Ruiz to head home from close range.
55th min: Spain look for a third, with Alvaro Morata's low shot just missing the target.
63rd min: Chance for Yamal to score a third for Spain, but the Barcelona attacker places his effort wide of the post from inside the box. Georgia just about survive in the contest.
68th min: Georgiy Tsitaishvili finds himself all alone inside the Spain box, but he fires wide of the post. Good chance for Georgia to level the scores.
74th min: Spain again have the ball in the back of the Georgia net, as Yamal's cross is turned into the back of his own net by Giorgi Gvelesiani, but it is disallowed for offside.
75th min: GOAL! SPAIN 3-1 GEORGIA (WILLIAMS)
Spain have their third of the match as Williams navigates his way into the Georgia penalty box before firing his effort into the back of the net from close range.
81st min: Smart save from the Georgia goalkeeper to keep out another Yamal attempt.
83rd min: GOAL! SPAIN 4-1 GEORGIA (OLMO)
Spain score a fourth in the 83rd minute through substitute Olmo, who takes a touch into the Georgia box before finding the bottom corner with an excellent strike.
FULL TIME: SPAIN 4-1 GEORGIA
MAN OF THE MATCH - NICO WILLIAMS
This was a very tough one, as Yamal and Rodri were also both excellent for Spain, but the award goes to Williams for his overall performance during the 4-1 success.
There is currently a host of speculation surrounding his future at club level, with the likes of Barcelona, Liverpool and Arsenal believed to be keen to sign the Athletic Bilbao attacker.
Williams set up Rodri for the Spain leveller, before he scored a spectacular goal himself in the second period, and there is no question that the youngster has been one of the players of the tournament thus far.
STANDOUT MOMENT
Yamal was unable to score in order to became the youngest goalscorer in the history of the European Championship, but he provided an assist - his second at the competition - for Ruiz to score, and it was spectacular.
Any player in world football would have been proud of the excellent delivery that he produced to set up Ruiz, let alone a 16-year-old in the very early stages of his career.
Yamal could have had two or three goals on another night, but he made a telling contribution, and it would not be a surprise to see the youngster go on to become the best player in world football in the not too distant future.
BEST STATS
MATCH STATS
Possession: Spain 73%-27% Georgia
Shots: Spain 34-4 Georgia
Shots on target: Spain 13-0 Georgia
Corners: Spain 13-3 Georgia
Fouls: Spain 11-5 Georgia
LINEUPS
SPAIN (4-3-3): Simon; Carvajal (Navas 81'), Le Normand, Laporte, Cucurella (Grimaldo 66'); Pedri (Olmo 52'), Rodri, Ruiz (Merino 81'); Yamal, Morata (Oyarzabal 66'), N Williams
GEORGIA (5-3-2): Mamardashvili; Kakabadze, Gvelesiani (Kvekveskiri 78'), Kashia, Dvali, Lochoshvili (Tsitaishvili 63'); Chakvetadze (Davitashvili 64'), Kiteishvili (Altunashvili 41'), Kocharashvili; Mikautadze (Zivzivadze 78'), Kvaratskhelia