Nishikori, who will take on either Juan Martin del Potro or Stanislas Wawrinka in the last four, is bidding to reach the final of this particular Grand Slam for the first time since 2014, when he lost to Marin Cilic.
It was a very comfortable first set for Murray, who held his four service games in addition to securing two breaks to claim the opener in just 37 minutes of tennis in New York.
Rain interrupted the second set and it was Nishikori that dealt better with the break as the 26-year-old broke back in the sixth, before breaking Murray once again at 4-5 to level the match at one set all.
An incredible third set saw five breaks of serve, including the opening two games as Nishikori continued to make it uncomfortable for the world number two, who recorded a 6-1 6-4 victory when the pair met at the Olympics last month.
The two players once again exchanged breaks in the latter stages of the set, but it was Murray that secured the decisive break at 4-4 before holding his serve to take a 2-1 lead in the quarter-final.
Murray had his eyes on the semi-final entering the fourth set, but Nishikori, who matched his opponent stride for stride, had other ideas, and a spectacular 6-1 set from the world number six saw him break twice on the way to levelling the match at 2-2.
Nishikori continued to impress as he broke Murray in the first game of the fifth set and after the Scot broke back, Nishikori broke again at 2-2 before holding to take a 4-2 lead in the final set.
The Japanese had a wonderful chance to move 5-3 ahead in the fifth when he met a low ball at the net, but he could not convert as Murray came from 40-0 down to move level at 4-4 in what was an incredible quarter-final.
Both players held their next service game, but Nishikori broke Murray for a third time at 5-5 to set up the opportunity to serve for the match, and the 2014 finalist took it to book his spot in the next round.