In her first victory against the Spanish on clay court, Halep struck a total of 19 winners and had huge advantage in winning percentage on first and second serve.
But Nishikori famously dumped the 2012 U.S. Open champion out in NY past year after rallying from two sets to one down.
"I didn't feel like I played great tennis today".
Speaking after the clash, Murray said: "He was dictating all the points in the first set, making me move a lot".
Nishikori won a dramatic five-setter 1-6, 6-4, 4-6, 6-1, 7-5 to reach the semifinals at Flushing Meadows.More news: London fire: Banned building materials suspected in Grenfell Tower
The world number nine said of his opponent: "We have played so many times".
Women's 4th rd: Elina Svitolina (Ukr) bt Petra Martic (Cro) 4-6 6-3 7-5, Simona Halep (Rom) bt Carla Suarez Navarro (Esp) 6-1 6-1.
"I don't know how I got the second and third". "It's not like I played a great point the next point".
But the 30-year-old - despite being broken on a couple of occasions - was never truly troubled and a combination of brilliant defensive work and a superior clinical edge meant Murray booked a last-eight meeting with either Kei Nishikori or Fernando Verdasco.
The Scot will now face the tournament's 2015 victor Wawrinka, who beat Marin Cilic 6-3, 6-3, 6-1, in what is a repeat of last year's semi-final showdown which Murray won in four sets before losing to Novak Djokovic in the final.
Wawrinka has not dropped a set on his way to the semis, and his 6-3, 6-3, 6-1 win on Wednesday over Marin Cilic was every bit as impressive as it sounds.
The Romanian will play Karolina Pliskova in the last four after the world No3 dispatched Caroline Garcia 7-6 (7-3), 6-4 in yesterday's other last-eight tie.
The Scot set up a semi-final rematch with third seed Wawrinka after beating the Swiss in four sets at the same stage of the tournament a year ago. "It's possible that I'm playing too slow". "Kei, you know, obviously lost against him at the US Open". Stan's obviously a big, strong guy, likes to go for his shots and he's obviously played really well in this tournament.