Zverev had his opportunities to get a stranglehold on the contest but failed to force Djokovic to capitulate as the world No1 won 6-7, 6-2, 6-4, 7-6.
The 33-year-old looked less hampered by his injury – despite the fact both he and Zverev had strapping on their respective stomachs – more by the barrage of shots from the German, who was Djokovic-esque at times in terms of getting the ball back in play.
But his inability to have beaten any of tennis’ big three continues, although his quarter-final performance into the early hours in Melbourne suggests he is not far off.
There were all manner of key turning points. Zverev had a set point in the hour-long opening set tiebreak but could not convert it, and was then invisible in a one-sided second set lasting half the time.
But he bounced back in set three to race into a 4-1 lead, a passage of play in which Djokovic smashed his racket to smithereens in frustration. And yet Zverev produced two double faults in one service game – his first in the opening two hours of play – in game eight to hand the ascendancy back to the Serbian.
Zverev again had opportunities in what proved the final set, even a break and set point at 6-5 only for a Djokovic ace to save it before the eight-time Australian Open took the resultant tiebreak and the match with his 23rd ace of the night.
But the Russian’s cause was helped by a back spasm which left his Bulgarian opponent virtually unable to serve in the third set of a 2-6, 6-4, 6-1, 6-2 defeat on day nine of the Australian Open.
Not even a medical timeout could properly rectify the problem for Dimitrov, who was never quite the same prospect from the start of that third set and cut a sorry sight as he limped off in pain at the end of the match.
Karatsev, the world No114 has been beset by his own injury problems, a long-term knee injury having curtailed his chances on the men’s tour.
And he had to come through the qualifiers to make the main draw, and will be joined in the last four by at least another Russian with countrymen Andrey Rublev taking on Daniil Medvedev in their quarter-final on Wednesday.
After his preceding round win, Andre Agassi had likened his ascent to a League Two side in English football beating Premier League opponents.
And of his history making, Karatsev said: “It’s an unbelievable feeling. I’m really surprised I’m here.
“It’s my first time playing main draw so it’s incredible. It was really tough for me to hold the nerves. Then in the third set he felt the back. I’m just trying to just go from match to match.”