Both Georgia and Spain entered the contest at RheinEnergieStadion in Cologne in high spirits after advancing from the group stage, the former progressed courtesy of a third-placed finish in Group F after beating Portugal in their final group fixture.
Spain, meanwhile, won all three Group B matches to qualify in first position, but their winning streak was at risk of coming to an end as Georgia took a surprise lead thanks to an 18th-minute own goal from Robin Le Normand.
However, La Roja resorted parity on the stroke of half time through midfield star Rodri, before the comeback was completed just six minutes after the break courtesy of a close-range header from Fabian Ruiz.
Spain eventually cruised to victory in dominant fashion, boasting 76% possession and firing 35 shots on goal compared to Georgia's four (none of which were on target).
Nico Williams capped a magnificent display with a sweet strike to double Spain's advantage, eight minutes before substitute Dani Olmo slotted home a fourth to send Luis de la Fuente's side into the quarter-finals.
Mamardashvili, who has now made twice as many saves (29) as any other goalkeeper at Euro 2024, is familiar with many of the Spanish players as he plies his trade at club level with La Liga side Valencia.
The 23-year-old has now predicted Spain to become European champions for an unprecedented fourth time, and win this summer's tournament for the first time since 2012.
Mamardashvili: 'Spain are Euro 2024 favourites'
"I think Spain are the favourites for this tournament and they will become champions," Mamardashvili told reporters as quoted by Reuters.
"It's a pity that we met this team, but it's okay, it's not the end. We will come back stronger. Of course, it's sad that we lost in the round of 16, but we should also be happy about it, because not long ago we couldn't have imagined that we would reach this far.
Reacting to Spain's win over Georgia, head coach De la Fuente told UEFA.com: "[My half-time] message was the same as I'd been telling them throughout the first half. Calm, no anxiety, no stressed decisions.
"I wanted them to seek the right moments to attack, to seek some calm in the match. I saw some anxiety growing when we didn't score, which can lead to negative tension, and I wanted them to get that out of their heads."
Spain will now prepare to test their mettle against fellow three-time Euros winners Germany in the quarter-finals; Die Mannschaft topped Group A before beating Denmark 2-0 in their last-16 tie.