The fifth seed, a quarter-finalist at Roland Garros last year, had too much in his armoury for 40th-ranked Kuznetsov on a sun-bathed Court One, although he made a slow start.
He dropped serve in the third game of the match when he drove a forehand long, but broke back quickly with a rasping backhand to finish off a fierce 24-stroke rally.
Another break of serve secured the set.
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Kuznetsov served a double-fault to gift Nishikori a break in the fifth game of the second set and the Japanese player moved 5-2 ahead with some punishing ground strokes.
A lapse in concentration allowed Kuznetsov to break back but that was only a minor inconvenience as Nihsikori broke the Russian's serve in the next game with sweetly struck forehand winner.
Nishikori was playing well inside his comfort zone as he eased through the third set and sealed the win with another sublime backhand pass.
"After going 3-1 down I tried to change it up a little bit and it started working better," he said.
"Second and third I think I played pretty good tennis."
Nishikori, whose only defeats on clay this year came in the Barcelona final against Rafael Nadal and in Madrid and Rome where he was stopped in the semis by Novak Djokovic, will face Spain's Fernando Verdasco in the third round.
Verdasco crushed Croatia's Ivan Dodig.
(Reporting by Martyn Herman, editing by Larry King and Ken Ferris)
