The Spanish defending champion, seeded a lowly sixth this year after a run of patchy form, showed the quality that has made him the dominant force on clay for a decade, brushing aside his opponent, ranked No 120, with relative ease.
He moves into the second week with an unblemished record and seems to be finding his best form in time for a likely quarter-final blockbuster with world No 1 Novak Djokovic – the man he has beaten in two of the last three finals.
Before that can become a reality he will have to beat American Jack Sock in the last 16.
“Things are going better,” Nadal said on court. “Against (Nicolas) Almagro (in the last round) I played a good match and again today I played well and had positive feelings.
“Fourth round is very good news for me.”
Apart from a dropped service game the first set was perfect for Nadal as he overpowered the lightweight Russian.
Kuznetsov did not hold serve until he was 3-0 down in the second set and although he began to make more of a match of it he was outclassed as Nadal improved his record at Roland Garros to 69-1.????
The last American man in the draw, Sock, surprised 18-year-old Borna Coric, who was looking to become the youngest player to make the fourth round of a major since Marat Safin reached the last-16 in Paris in 1998, 6-2 6-1 6-4.