The world number 114 was also only the fifth qualifier to reach the last four of a men's major in the open era and the lowest-ranked player to reach a Grand Slam semi-final for two decades.
The Russian, whose success at getting into the Australian Open came on his 10th attempt to qualify for a Grand Slam, will meet eight-times champion Novak Djokovic or Alexander Zverev for a place in the final.
"It's an unbelievable feeling, first time main draw, first time semis," said the 27-year-old, whose victory was marked only by canned applause with fans still banned from Melbourne Park because of a five-day coronavirus lockdown.
Dimitrov, who had not dropped a set on his way to the quarter-finals, said he had suffered a back spasm on Monday and struggled to put his socks on before the match.
"It sucks," the 29-year-old said. "It's sport, you just never know. That's why you have to keep on trying to the end.
"I give respect to the guy, as well. He saw me struggling and he kept on doing what he had to do."
Karatsev confessed to battling with nerves at the start of the contest on Rod Laver Arena and his error-strewn first set was indeed forgettable.
He had battled back from two sets down to beat Felix Auger-Aliassime in the fourth round, however, and soon tightened up his game to storm back into the match in the second stanza.
Dimitrov looked shell-shocked as Karatsev pounded howitzer shots over the net at him -- faltering on serve and wandering around the court listlessly in the 30 degree Celsius heat.
The 29-year-old Bulgarian took a medical timeout for treatment on his back after losing the third set but was only able to show flashes of his refined game in the fourth.
Karatsev showed no mercy to his hampered opponent and took a comfortable lead over the 18th seed, sealing his place in the last four when Dimitrov flapped a backhand into the net.
With his ATP Cup team mates Daniil Medvedev and Andrey Rublev facing off in a quarter-final on Wednesday, Russia are guaranteed to have two players in the semi-finals and could yet provide both finalists.
"I try not to think about it, I just look at the next match," said Karatsev when asked about the prospect.
