Nadal, 33, ultimately had too much quality for the Croatian 22nd seed in a 6-3 3-6 6-1 6-2 victory in New York.

Cilic, 30, briefly rediscovered his best form to level before wilting.

Nadal, the 18-time Grand Slam champion, will play Argentine 20th seed Diego Schwartzman in the last eight.

"For some moments in the second set I felt there were too many points in his hands, he was pushing me back, more aggression than me and he hit every ball very strong," said Nadal.

"After that second set I thought something needs to change or I would be in his hands. I started to return the second serve inside the court and that created a different perspective."

After 2018 champion Novak Djokovic retired injured from his last-16 match against Stan Wawrinka on Sunday, Nadal is considered the joint favourite for the men's title alongside Swiss great Roger Federer.

Nadal is aiming to close the gap to 20-time major winner Federer with his fourth title at Flushing Meadows.

The illustrious pair remain on course to meet in Sunday's final which, remarkably, would be the first meeting in New York of their enduring rivalry.

First Nadal must see off Schwartzman, who reached the last eight for the second time by beating German sixth seed Alexander Zverev.

Federer, 38, plays his quarter-final against Bulgaria's Grigor Dimitrov at about 02:00 BST on Wednesday.

Nadal's resilience - and brilliance - leaves even Tiger impressed

Golfer Tiger Woods, who has watched Roger Federer many times previously, was supporting Nadal on Arthur Ashe Stadium

Nadal encountered few problems in a straightforward opening set, only to see the powerful Cilic find his range in the second as he cut down on the unforced errors and pinned the Spaniard back.

Cilic has recently looked a shadow of the player who was a constant fixture inside the world's top 10, a knee injury in 2018 contributing to him sliding to his lowest ranking in more than five years.

That previous form returned as he pushed Nadal back with heavy groundstrokes and backed them up with pinpoint winners to level the match.

Yet the momentum was suddenly dragged away from him by some remarkable returning from Nadal in an exhilarating fourth game of the third set.

Nadal scurried forward to reach a drop shot and then produced a twirling overhead for 0-30, topping that by somehow returning a smash which Cilic should have buried before swatting away a cross-court backhand winner for three break points.

Golf great Tiger Woods, who was animatedly supporting Nadal throughout, leapt to his feet as Ashe rose to acclaim the sheer brilliance of the Spaniard.

A deflated Cilic limply handed over the break with a double fault, producing another as Nadal broke again for a 5-1 lead on his way to a two-set lead.

That familiar problem returned on break point in the first game of the fourth set, giving Nadal a crucial break which he doubled for a 4-0 lead after seeing off a break point.

All hope was lost for Cilic by that point, Nadal teeing up match point with a stretching forehand winner around the net post which left Ashe incredulous again before he wrapped up victory in two hours and 49 minutes.