It was a very watchable US Open match that went on into the wee hours in front of a passionate crowd.
Carlos Alcaraz won the first set after, among other things, making a senseless save when he lunged for the ball and got a stoppage.
Both continued to play well and the final two sets were high drama.
Cilic finally won the fourth and started by breaking the Spaniard's serve in the fifth.
But Alcaraz broke right back and then made a big impression as he won 6-3.
If the match had continued for three more minutes, it would have been the last match in the US Open's 141-year history, but now Mats Wilander against Mikael Pernfors from 1993 still stands as a shared record match.
The match took a total of 3 hours and 53 minutes.
The Norwegian can become world number one
With Rafael Nadal surprisingly going out in the fourth round, Alcaraz and the Norwegian Casper Ruud have the opportunity to become world number one after this tournament.
For that to happen, one of them must reach the final.
Whoever goes there will be world number one starting next week.
If they were to meet in the final, whoever wins becomes world number one.
If neither of them reaches the final, Nadal will take over the world number one title from Russian Daniil Medvedev.
If Alcaraz succeeds, he will become the youngest ever to claim the title of best in the world.
Ruud can become the first Norwegian to become number one.
Neither talent has won a grand slam tournament.