The world number three triumphed 6-0, 2-6, 6-2 over 2014 and 2015 champion Nishikori and next faces Britain's Cameron Norrie, a fellow left-hander, for a place in the semi-finals.
Japan's Kei Nishikori is the No 7 seed this year after reaching the semifinals in Flushing Meadows last year.
Federer and Nadal each won their quarter-finals to set up an epic semi-final between the two, whilst world number 1 Djokovic will face Bautista Agut for a place in the final.
Rafael Nadal showed no signs of rust as he raced into a 5-0 lead against fellow Spaniard Roberto Bautista Agut in the first set on Court Rainier III, defending his Monte Carlo Masters title with 6-1, 6-1.
Roger Federer was challenged by Fernando Verdasco before defeating the Spanish veteran 6-3 3-6 6-3, reaching the quarter-finals of the Dubai Duty Free Tennis Championships.
Madison Keys clinched her second consecutive semifinal berth by beating Carla Suarez Navarro 6-4 6-3 while Novak Djokovic beat Australian John Millman 6-3 6-4 6-4.
Tennis fans are dreaming of another final between Rafael Nadal and Roger Federer as the two have stormed into the Wimbledon quarterfinals on 'manic Monday', when all 16 fourth-round singles matches are played.
The carnage of seeds at the world's premier grass court tennis tournament continued, with only one of the top 10 women's seeds remaining in the tournament at the fourth round.
Alexander Zverev overcame Russian in five sets while Austrian Dominic Thiem downed Japan's Kei Nishikori in four sets.
Nadal and Djokovic have played each other 50 times, but their last meeting came more than a year ago, when Nadal won in the Madrid Open semifinals. Djokovic leads Nadal 26-24 overall, but Nadal holds a 13-7 advantage on clay.
Rafael Nadal easily reached the trophy over Kei Nishikori with a 6-3, 6-2 win and became the first man in the Open era to win the same title 11 times.
World number one Andy Murray beat Kei Nishikori 2-6 6-1 7-6(0) setting up a tough semifinal against former French Open Champion Stan Wawrinka who beat Marin Cilic 6-3 6-3 6-1.
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