The 18th seed won 5-7, 6-2, 6-4 against an out-of-sorts Alcaraz as the Bulgarian steps up his pursuit of a first ATP title since 2017.
He will next face the 22nd-seeded Nicolas Jarry (28) after the Chilean defeated wildcard Diego Schwartzman (31) 6-3, 5-7, 6-3.
The first Shanghai Masters since the pandemic has opened up for Dimitrov after the early exits of Daniil Medvedev, Stefanos Tsitsipas and Holger Rune.
World number one Novak Djokovic (36) is not in China.
"I'm still here, I'm not going anywhere," Dimitrov said afterwards.
Spain's Alcaraz, the world number two, was chasing a seventh tour-level title of the season but he uncharacteristically crumbled after winning the first set.
Alcaraz took time to find his range and Dimitrov broke for 3-2 in the first set with a vicious whipped forehand return.
Dimitrov was broken back as he served for the set in a riveting 10th game involving two thrilling rallies that both times saw Alcaraz come out on top.
Alcaraz held and then broke again to wrap the set up in just under an hour.
But rather than power on to victory, Alcaraz let the match get away from him.
Dimitrov gathered himself to race into a 2-0 lead in the second set, then broke again for 5-2, before sealing the set when Alcaraz shanked his return.
They went to a decider and an unusually flustered Alcaraz was broken in the third game after yet another unforced error.
Alcaraz let out a roar of anger as the match slipped away from him.
Dimitrov held his nerve to serve out his first victory over the Spaniard on his second match point.
"In the third set it was a bit cat and mouse," said Dimitrov.
"I knew I had to apply constant pressure on him."
"Even if I was down, even if my shots were not good enough, I had to put him in uncomfortable positions.
"He doesn't like being on the back foot."
"He was on another level today, this Grigor," said Alcaraz, who lost to Sinner in the semi-finals in Beijing and won't look back on his visit to China with much fondness as a result.
"I was all the time defending, I could not find the way to put myself in a position to attack."
The efficient Andrey Rublev (25) beat the American 12th seed Tommy Paul (26) 7-5, 7-5 in their last-16 encounter in the late-night match.
Rublev meets Ugo Humbert (25) of France in the quarter-finals after the 32nd seed demolished J.J. Wolf (24) of the United States 6-1, 6-2 in just 57 minutes.
