The Spaniard, a nine-time winner at Roland Garros, was sensational throughout this lopsided contest, eventually winning 6-0, 6-1, 6-0 against the Georgian. In Round 4 the King of Clay will take on compatriot Roberto Bautista Agut.
Second seed and 2016 winner Novak Djokovic didn't have things so easy, needing five sets to overcome Diego Schwartzman.
In the women's draw, fourth seed and defending champion Garbine Muguruza continued to build momentum and improved throughout her win against Yulia Putintseva. Svetlana Kuznetsova, seeded eighth, and Venus Williams, seeded 10th, also picked up wins.
Here are the results in full from Friday's action and a recap of another memorable day at a fascinating French Open.
(19) Albert Ramos Vinolas bt. (16) Lucas Pouille, 6-2, 3-6, 5-7, 6-2, 6-1
(2) Novak Djokovic bt. Diego Schwartzman, 5-7, 6-3, 3-6, 6-1, 6-1
(6) Dominic Thiem bt. (25) Steve Johnson, 6-1, 7-6 (4), 6-3
(4) Rafael Nadal bt. Nikoloz Basilashvili, 6-0, 6-1, 6-0
(20) Pablo Carreno bt. (11) Grigor Dimitrov, 7-5, 6-3, 6-4
(17) Roberto Bautista-Agut bt. Jiri Vesely, 6-3, 6-4, 6-3
Horacio Zeballos bt. (10) David Goffin, 4-5 (retired)
(5) Milos Raonic bt. Guillermo Garcia-Lopez, 6-1, 1-0 (retired)
(10) Venus Williams bt. Elise Mertens, 6-3, 6-1
(8) Svetlana Kuznetsova bt. (32) Zhang Shuai, 7-6 (5), 4-6, 7-5
(13) Kristina Mladenovic bt. Shelby Rogers, 7-5, 4-6, 8-6
(23) Samantha Stosur bt. Bethanie Mattek-Sands, 6-2, 6-2
(4) Garbine Muguruza Blanco bt. (27) Yulia Putintseva, 7-5, 6-2
Jelena Ostapenko bt. Lesia Tsurenko, 6-1, 6-4
In Round 3 of any Grand Slam tournament, there are no easy matches. But Nadal makes tennis look so simple on clay, much to the misfortune of Basilashvili, who is ranked a creditable 63rd in the ATP world rankings.
With bagels bagged in the first and third set, Nadal had his triumph summed up by Ben Rothenberg of the New York Times in visual format:
Remarkably, it took just 90 minutes for Nadal to come through this one and secure his place in Round 4, playing some mesmerising tennis along the way. He conceded just 36 points overall.
Having struggled to show his best at Roland Garros in recent outings, it's clear he's back in his absolute pomp once again. Basilashvili was daunted by taking on the nine-time champion on the big stage, but Nadal didn't give him a chance to settle, showcasing raw power and breathtaking invention throughout the match.
As noted by tennis journalist Ash Marshall, even for a man of Nadal's experience and pedigree, this result was a pretty special one:
Djokovic had to dig deep to get through his match, coming from behind twice to eventually see off Schwartzman.
The second seed started well, although his opponent was playing with freedom and finding the lines. It meant Djokovic was forced to cling on, as the Argentinian moved to within one set of a memorable victory.
The champion had gears to go through, though, and with his tournament status in doubt, he really turned it on, winning the final two sets for the loss of a couple of games. Per the tournament's official Twitter feed, there aren't many men who have won more matches at this venue than Djokovic:
Muguruza, meanwhile, is in an excellent position to defend her crown at Roland Garros, as she ground down Putintseva.
While there were some doubts about the fitness of the Spaniard ahead of the French Open, the champion has showcased so much determination to make it through three matches in Paris.
As noted by the WTA Insider Twitter feed, next up for Muguruza is an equally diligent player in Kristina Mladenovic, who somehow still has a chance of winning this tournament:
Also in with a shout is Kuznetsova, although she made hard work of her match against Zhang Shuai.
All three sets were fiercely contested in this one, with neither player giving an inch throughout. However, when the pressure came late in the third stanza, it was the class of Kuznetsova that came to the fore. Per tennis journalist Ilya Ryvlin, the two-time Grand Slam winner was not pleased with her performance despite the win:
Williams would have been pleased with her effort, making light work of Elise Mertens on Philippe Chatrier Court.
The 36-year-old has yet to drop a set at this tournament and looks to be in excellent form on the Roland Garros clay. With her sister Serena absent due to pregnancy and top seed Angelique Kerber eliminated already, the veteran may not get a better chance to clinch the first French Open win of her incredible career.