The 20-year-old American is the son of former Grand Slam champion Petr Korda who won the 1998 Australian Open and made the 1992 French Open final before losing to American Jim Courier.
Korda began the match unfazed at playing the 12-time French Open winner on Court Philippe-Chatrier as he took Nadal to deuce in the Spaniard's opening service game.
Two break points came and went for Korda as a body serve and some stealthy tactics from Nadal ushered a few unforced errors from the American's racquet, as the 19-time Grand Slam champion took the opening game after nearly 10 minutes.
Korda looked nervous in the early exchanges as a tidy net volley swept Nadal into a 3-0 lead within 25 minutes.
The gusty weather conditions also made life difficult for both players as they battled to adapt.
Some stodgy footwork from Korda and a double-fault gave Nadal a second break of serve as he raced into a 4-0 lead within 25 minutes.
The 34-year-old Spaniard then produced his trademark moonball forehand winner to go 5-0 up on his younger opponent, 14 years his junior.
Korda then finally got on the scoreboard as a few uncharacteristic Nadal errors gave him a love service hold.
However, it was not enough as the wind continued to play havoc as Korda went long to give Nadal the opening set 6-1 in 37 minutes.
The second set continued in the same fashion as the first as the Spaniard secured the early break and reinforced it with an easy hold of serve.
Nadal then continued to delight the small cluster of fans on Chatrier as he soon moved through the gears to go 3-1 up in the second.
Korda then produced his best moment of the match with a fine stop volley to demonstrate net skills worthy of his father's applause.
However, a combination of naive shot-making and poor footwork skills saw the American slap a backhand long to give Nadal another break and with it a 4-1 lead.
The Spaniard then turned on the style with some fine shot-making as fabulous sliced drop shot winner helped put Nadal 5-1 up and coasting towards the second set.
Under the watchful eye of his coach and former 1998 French Open champion, Spaniard, Carlos Moya, Nadal cracked an amazing forehand winner up the line, in arguably the point of the match to take the second set 6-1.
With the pressure off and two sets to love down, Korda's shoulders relaxed as he began to swing freely and he dispatched a fine backhand volley to secure his first break of the match.
Nadal looked flustered as the wind began to unsettle the Spaniard's usually reliable clay-court game.
Korda was able to take full advantage of this blip in form as he worked the Spaniard left and right before a fine drop shot volley drew applause from his hero.
In a game lasting six minutes, Korda produced a booming backhand winner down the line at deuce to bring up advantage. But the resilient Spaniard battled back to deuce before a ferocious forehand winner and a classy backhand gave the American a surprising 2-0 lead at the beginning of the third.
With the wind getting stronger, Nadal knew he had to dig deep as he was taken to deuce giving Korda a sniff at another break. However, two unforced errors from the American put Nadal back into his stride as he took his first game of the set.
A beautiful drop shot from the back of the court from the 20-year-old American earnt a bravo from Rafa, but it was not enough as the defending champion roared back to two games all.
The Spaniard could sense the finish line was close as he sealed a love service hold to move 3-2 ahead.
Nadal began to turn the screw as a fine drop shot from the back of the court helped secure a 4-2 lead and in winning 14 of the last 15 points, a second successive break of serve for the Mallorcan.
"The King of Clay" was on a roll as Nadal won six consecutive games to seal a 6-1, 6-1, 6-2 triumph, and with it a place in the quarter-finals.
What it means for Nadal
The victory gives the 19-time Grand Slam champion his 97th French Open win as he moved 97-2 at Roland Garros.
He has coasted into the second week of the French Open without dropping a set after convincing wins over Belarus' Egor Gerasimov, American Mackenzie McDonald, Italy's Stefano Travaglia, and now America's Sebastian Korda.
With plenty of energy in the tank, the 34-year-old must really fancy his chances now of first autumnal French Open title.
Next up for Nadal is 19-year-old Italian, Jannik Sinner, who defeated US Open finalist Alexander Zverev in four sets to win 6-3, 6-3, 4-6, 6-3 in just over 3 hours.
Sinner becomes the first French Open debutant to make the quarter-finals since Nadal himself back in 2005 as the Mallorcan would go on to beat Mariano Puerta and win a first Grand Slam title.