Nadal who is seeking an 11th title in Monte Carlo, emerged from his 79 minute match and declared that he needs more competitive matches to restore his confidence ahead of a tilt at an 11th French Open title in Paris in May.
"The win against Bedene is a positive start, of course," he said. "It's important for me to win matches. I need days on court.
"Every match that I have the chance to win is great news because it's confidence and is a chance to play another day, and that's what I need."
The 16-time Grand Slam winner, like ninth seed Novak Djokovic, is seeking a record 31st title in a Masters event - considered just below the Grand Slam tournaments in terms of prestige and ranking points.
Khachanov, touted as one of the emerging stars on the circuit, cruised past the French veteran Gilles Simon 6-2 6-2 to reach the last 16.
Japan's Kei Nishikori continued his comeback from injury with an impressive 7-5 6-2 win over Daniil Medvedev from Russia.
The former world number four, who has struggled over the last year with an injury to his right wrist, followed up his first round victory against Tomas Berdych with a gritty display on centre court.
"The first set was a real battle," said Nishikori. "He was playing a little better than me at the beginning. I just tried to stay calm and not do anything too crazy and stay calm at the baseline."
Second seed Marin Cilic advanced to the last 16 following a straight sets win over Fernando Verdasco. The Croatian will play the big serving Canadian Milos Raonic for a place in the last eight.