The 70th-ranked Purcell has produced some of the best tennis of his career recently and at the US Open tune-up event he took down French Open finalist Casper Ruud and three-time Grand Slam winner Stan Wawrinka of Switzerland.
But Alcaraz's superb form was too much to overcome as the twice Grand Slam winner kept his cool after a frustrating opening set, unleashing 30 winners in the match on Centre Court.
"He (impressed) me a lot. His game is pretty good. Serve really well. Volley pretty well, as well. It was really tough for me," Alcaraz told reporters.
The Spaniard failed to convert his only break point chance of the first set in the second game before helping Purcell to the crucial break in the seventh game with an unforced error.
Purcell sealed the first set with an unreturnable serve but the 20-year-old Spaniard sent a quick reminder of why he is the world's best as he won the first three games of a speedy second set, where he dropped only two of his first-serve points.
Down a break in the third, Purcell refused to go down without a fight, fending off four break points in an epic third game before neutralising Alcaraz's mighty forehand to break back in the fourth.
But the Wimbledon champion kept his composure and broke Purcell to love in the ninth game before sealing the affair in the next game with an ace and a smile.
"I feel like I'm playing well. Obviously not my best. I can increase my level, of course," said Alcaraz.
"But I feel the opponents, when they are playing against me, I'm going to say, well, they play a little bit better. Obviously, I will say that you can be better every day."
The win set up a semi-final with Poland's Hubert Hurkacz, who sent over 10 aces and never faced a break to get past Australian lucky loser Alexei Popyrin 6-1 7-6(8).
Hurkacz, who lost to Alcaraz in the last 16 in Toronto earlier this month, won the first five games in the 26-minute first set, where he only dropped one first-serve point.
He squandered a 6-1 lead in the tiebreak but held on to reach the fifth Masters 1000 semi-final of his career.
"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."
Capping the evening's programme, second seed Djokovic converted on all five break point opportunities to flummox Fritz in a clinical performance, sending over 13 winners while making few mistakes.
He needed only 21 minutes to cruise through his opening set against an increasingly frustrated Fritz, who struggled in virtually every aspect of his game as he put up a trio of double faults with a malfunctioning serve.
The 23-times major winner only briefly appeared vulnerable as a resolute Fritz converted on a break point in the opening game of the second set. But a steely Djokovic kept his calm and broke back in the eighth, leaning on his reliable forehand.
The Serbian closed out the affair in about an hour, breaking Fritz's serve in the 10th game with a crosscourt forehand shot that the American was unable to return.
He next faces German number 16 seed Alexander Zverev, who never faced a break point as he comfortably beat France's Adrian Mannarino 6-2 6-3 early in the day.
