For a moment Max Purcell and his supporters dared to dream.
Playing a scintillating brand of serve-and-volley tennis, with powerful serving and excellent net play, the Aussie battler threatened an upset that would have gone far beyond Ohio to turn heads across the tennis world.
But reality, and the young Spaniard's brilliance, intervened. And perhaps fatigue after a demanding fortnight for the 25-year-old Sydneysider.
Alcaraz eventually came through 4-6 6-3 6-4 to move into the Cincinnati Open semi-finals and a meeting with Poland's Hubert Hurkacz, who earlier on Friday had ended Alexei Popyrin's run to the last eight.
But the reigning US Open and Wimbledon champion knew he had been in a game.
Playing his 10th match in 12 days, plus a demanding journey across the 49th parallel, world No.70 Purcell looked beaten at 0-40 and 0-2 down in the final set.
But he held, then broke and held again, to be 3-2 up. He led again 4-3, but was broken and went 4-5 down. Even then he had a break point for 5-5, but a rare loose forehand let Alcaraz off the hook and the 20-year-old took full advantage ending the two-hour, 11-minute match with an ace.
The match had begun as expected, Alcaraz holding to 15 then forcing a break point. But Purcell held, then traded games to 3-3 before pouncing on a double fault that had gifted a break point to take a 4-3 lead.
He then held to 30 twice to take the set 6-4 in 43 minutes.
Alcaraz, is a fast earner and he adjusted tactics. All too soon he was 3-0 up in the second before efficiently wrapping up the set.
At 2-0 the third set looked as if it would go the same way, but Purcell never took a backward step. Alcaraz's roar of delight upon victory made it clear how hard he had been pushed.
Nevertheless, Purcell had much to encourage him as he looks towards what will be only his second appearance in the US Open main draw.
Making his performance in Ohio even more creditable the journey to the last eight had been anything but simple.
After reaching the last 32 in Toronto last week he had a dash to make qualifying in Cincinnati. With no direct flight he took an Uber to the Canadian-US border, but was left there as his driver would not cross it. Eventually he made it to Detroit, but could not get a drive to Cincinnati.
He finally got a flight, but arrived too late to practice ahead of qualifying.
Nevertheless, he won through two rounds of qualifying, then three in the main draw during which he put out world No.7 Casper Rudd and former grand slam champ Stan Wawrinka. There is much to build on.
Earlier Hurkacz beat Popyrin 6-1 7-6 (10-8).
Popyrin had lost to Purcell in qualifying in Ohio, but was restored to the draw as a 'lucky loser'. He had capitalised on his fortune to make the quarters but a slow start against the Pole left him chasing the match after losing the first set in 25 minutes.
The second set went with serve but in the tiebreak Popyrin found himself 1-6 down. He saved five match points and forced a set point of his own. But Hurkacz saved it with an ace and went on to take the match.
"Alexei raised his level and was serving really good throughout that second set, I just got to the tiebreaker," Hurkacz said.
"I got off to a good start and then Alexei played some good points, but fortunately I battled through for that one."