The 19-year-old Alcaraz triumphed 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 before the final end of the tournament.
Alcaraz, the top-ranked player remaining in the men’s draw, will play his second US Open quarterfinal when he takes on Jannik Sinner on Wednesday.
“It was incredible,” Alcaraz said in his on-pitch interview. “After the fourth set I had a lot of chances in the end and lost the fourth set.
“It was hard for me to come back in the fifth set, to stay mentally strong, but … the energy I received today (from the crowd) pushed me to the win.”
Against Cilic, Alcaraz led after the first and third sets in a match that lasted almost four hours, but failed to knock out his Croatian opponent until the fifth.
He broke serve early in the game but fought back to win the next four games and win the opener.
There was a similar story in set number two as Alcaraz broke early before Cilic unwound four straight games and held serve to level the match.
The third set held serve until Alcaraz broke 5-4, but his 2-1 lead was cut when Cilic broke late in the fourth set – despite the teenager having break points of his own throughout the set.
With the game going well past midnight, Alcaraz capitalized on the advantage with a break to make it 2-1 and sealed the win when Cilic slammed a forehand into the net.
This was by far the toughest test of the tournament so far for Alcaraz, who hadn’t lost a set before facing Cilic.
He next meets another rising star in 21-year-old Sinner – the Italian who, like Alcaraz, is hoping to reach a Grand Slam semi-final for the first time.