Alcaraz, 19, prevailed 6-4 3-6 6-4 4-6 6-3 in a match that ended at 2:23 a.m. local time, just three minutes from the final end of the tournament.
Alcaraz, the highest-ranked player remaining in the men’s draw, will play in his second US Open quarter-final when he takes on Jannik Sinner on Wednesday.
“It was amazing,” Alcaraz said during his on-court interview. “After the fourth set I had a lot of chances at the end, I lost the fourth set.
“It was difficult for me to come back in the fifth set, to stay strong mentally, but… the energy I received (from the crowd) today made me win.”
Against Cilic, in a match that lasted nearly four hours, Alcaraz led after the first and third sets but couldn’t keep their Croatian opponent away until the fifth.
He broke serve early in the game but fought back to win the next four games and take the opening set.
There was a similar story in the second set as Alcaraz broke early before Cilic had four straight wins and held serve to tie the game.
The third set stayed on serve until Alcaraz broke at 5-4, but their 2-1 lead was cut when Cilic broke late in the fourth – although the teenager had his own points breaks throughout the set.
As the game continued well past midnight, Alcaraz took the lead with a break at 2-1 and sealed the victory when Cilic hit a forehand into the top of the net.
It was by far the toughest test of the tournament so far for Alcaraz, who hadn’t dropped a set before facing Cilic.
He will next face another rising star in 21-year-old Sinner – the Italian, like Alcaraz, hoping to reach a Grand Slam semi-final for the first time.
