The win, along with compatriot Naomi Osaka's earlier one-sided 6-1, 6-1 triumph over Lesia Tsurenko, means Japan have a men's and women's semi-finalist at the same Grand Slam for the first time in the professional era. In her third-round match, she was even quicker, dominating Aliaksandra Sasnovich, 6-0, 6-0, in 50 minutes.
The Japanese sputtered along until earning his first break chance at 2-4 in the second set and was able to convert to get back on serve.
Naomi Osaka won her quarterfinal in the match that preceded Nishikori's.
Osaka, who is just 20 years old, is having a terrific 2018 season.
"I think (Osaka and Williams) really are different people, because the only similarity they have is that they kind of have the same hair, big hair", Bajin said, smiling.
The Croatian has built on that success, reaching two more finals in the last two seasons, but Nishikori's only similar run came in NY two years ago when he defeated Andy Murray to reach the semi-finals before losing to Stan Wawrinka.
Osaka was smooth and confident as she won the first set 6-3.
Tsurenko had dealt with heat issues in the fourth round, when her opponent accused her of acting, and said after her lopsided loss to Osaka that she was dealing with a sore throat and problems breathing. Cilic started well, taking the opening set and going up a break in the second.
Even in the final set Nishikori looked comfortable with a 4-1 lead before Cilic levelled, only for the Croat to lose the final two games. I try to fight every point even though I was really exhausted.
"Today was not my day, obviously", Tsurenko said.
She was quickly down two more breaks at 4-0 before squandering three break points in the sixth game as Osaka glided into a maiden semi-final at the Slams. "I was not feeling well", she said.
Tsurenko laboured in the heat during her fourth-round victory over Marketa Vondrousova, having her temperature and blood checked during a medical timeout in the first set and almost quitting when she trailed early in the second.
Tsurenko didn't appear bothered by the conditions, but whether it was her health or just first-time jitters, she was off from the minute she stepped onto Arthur Ashe Stadium.
The crisis soon deepened for Tsurenko, who had needed the best part of three hours on Monday to beat Czech teenager Marketa Vondrousova in a match where she nearly collapsed due to heat exhaustion.