Nadal, who like Woods has endured more than his fair share of injury nightmares, looked healthy and hungry at Flushing Meadows, where he is chasing a fourth US Open title after 2010, 2013 and 2017.
Cilic would double fault later in the game to give Nadal a 3-1 lead and he would never threaten again on a hot and humid night in NY, with Tiger Woods among the star-studded crowd at Arthur Ashe Stadium cheering on the Spaniard.
Nadal will take on Diego Schwartzman after sixth seed Alexander Zverev ran out of steam in his bid to reach the quarter-finals for the first time.
In the stands, Woods allowed himself a smile.Nadal, who has a mean golf game, with a single digit handicap, said he hadn't asked the American for advice.
"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.
"I hit it well but to hit that spot, of course you need some luck". "I always say I never had big idols, but I have to say one idol is him".
"For me, it's a big pleasure to have him here supporting". He's a big legend of the sport, one of the greatest sportsmen of all time.
Rafael Nadal (pictured left) had Tiger Woods (pictured right) off his chair. "I just want to congratulate him for one of the more wonderful comebacks ever in sports, winning the Masters this year". 'Maybe he can lose a little bit of rhythm after that'.
Then again both were later surpassed by the sprinting, sliding, bend-it-around-the-net-post forehand victor to get to match point, which Woods loved too.
"I know people can think that Zverev was favored before that match".
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. 'But neither of us heard me getting a warning in the first place. I think still it's been a positive season.
The diminutive Argentine has faced Nadal seven times and lost every meeting but has proven a hard test in the slams, forcing the Spaniard to go four tough sets at the 2018 Australian and French Opens.