Tsitsipas, winner in Monte Carlo in 2021 and 2022, needed just 81 minutes to record his eighth win in nine meetings with an out-of-sorts Khachanov.
The 25-year-old Greek will meet the winner of the quarter-final between Holger Rune and Australian Open champion Jannik Sinner.
"I was very effective from the start, I had a lot of pace and gained momentum," said Tsitsipas.
"I tried to do my part and press and it worked out really well."
Khachanov had cheekily said to the umpire prior to the match, "Are you going to stay focused?" to which the official replied, "Always, of course."
It was Khachanov who should have asked himself the question as he rarely seemed to be and was way off the form he had shown in Thursday's defeat of compatriot Daniil Medvedev.
The opening exchanges were messy from both players with three successive breaks of serve - Tsitsipas breaking the run to open up a 3-1 lead.
Khachanov finally won a service game of his own to make it 3-2 displaying a fine mix of power hitting, delicate touch and agility. However, he required medical attention at the changeover at 5-4 down, returning to the fray only for Tsitsipas to serve out the set.
Khachanov, who seemed to be troubled by a pain in an upper quad, came under pressure on his serve at 1-1 in the second set, but he saved a break point and then held.
However, it was a very unhappy Khachanov who returned to his chair at the next changeover as a series of errors gave his Greek rival the break at 3-2. The 27-year-old Russian flung his racket angrily to the ground as he took his seat.
Tsitsipas did not ease up winning 11 points in a row to surge to a 5-2 lead and served out easily for a place in the last eight.
He admitted the tournament brought out the best in him, though it is yet to lead to him winning the big one on clay, The French Open.
"I would lie if I said it did not bring out the best in me," he said grinning.
"There are many good memories and stepping out here and coming back here, it revives those good memories. It brings me alive."
