The fourth seed required just 72 minutes to see off the challenge of his Spanish opponent, breaking the 14th seed on three occasions.
Nishikori got off to a fast start, securing the first break of the match in just the third game before holding his serve to take the opener 6-3.
The second set went according to serve until the eighth game when Nishikori manufactured another break to seize the initiative. Having edged ahead, the Japanese ace then broke Bautista Agut once more in the ninth game to take the match 6-3, 6-3.
Speaking after the match, Nishikori, who was a beaten finalist at the event last year, said that he is pleased with where his game is at present.
“I was feeling really comfortable out there,” said Nishikori. “[I was] really happy the way I'm playing today.”
Nishikori will face David Ferrer in the quarter-finals after the Spaniard defeated compatriot Fernando Verdasco 5-7, 6-3, 6-4. The duo faced off in the semi-finals of the tournament last year, with Nishikori victorious. However, Ferrer will be boosted by the fact that he downed the world number five in the final of the Mexican Open earlier this year.
In other matches on Thursday, Rafael Nadal, Andy Murray, Tomas Berdych, Milos Raonic, Grigor Dimitrov and John Isner all booked their places in the last eight.