The City midfielder grabbed his nation’s first goal with a clinical drive from the edge of the area to draw La Roja level.
Spain had caught the eye during the group stages and went into the tie with the only 100% record left in the tournament.
But that was put to the test when, despite dominating early on, Georgia took a shock lead on the counter attack.
Having weathered the storm for 17 minutes, they made their first foray forward count when Otar Kakabadze’s vicious ball in from the right was deflected into the Spain net by Robin Le Normand, under pressure from Khvicha Kvaratskhelia.
Normal service resumed soon after, with Rodrigo setting up Fabian Ruiz for a vicious near-post strike, which was smothered by Giorgi Mamardashvili.
But the City midfielder would eventually be the man to break Georgia’s resistance as half-time approached.
Picking up play on the edge of the area from Nico Williams, the Spaniard dragged the ball back across his body onto his weaker left foot and rifled a vicious low drive into the bottom corner.
Spain would then take the lead, despite a brief scare from an audacious Kvaratskhelia half-way line effort, six minutes after the restart.
Exciting 16-year-old Lamine Yamal’s cross from the right was inch-perfect for Ruiz, whose headed effort trickled past Mamardashvili.
Alvaro Morata’s substitution midway through the second half meant Rodrigo toom over the captaincy, and La Roja should’ve been out of sight by the midway point in the half when Yamal twice went close from a promising position.
But the third would come with 15 to play when Williams fired into the roof of the net after skipping away from Giorgi Gvelesiani on the counter.
Rodrigo was brought off soon after, resting up ahead of Spain’s last eight clash with host nation Germany on Friday 5 July, with Dani Olmo adding a fourth late on to round off another impressive performance from the three-time European champions.
