The twice Roland Garros champion could not find a weakness in the 11th-seeded Khachanov's serve at first, but once he took the second set tiebreak there was no looking back for the Serbian.
He will be closely watching Tuesday's night match between world number one Carlos Alcaraz and fifth seed Stefanos Tsitsipas, whose winner will be the last man standing between him and a seventh French Open final.
On a Court Philippe Chatrier gradually being covered by the shade, the veteran did not have a single break opportunity and looked a tad slow in the opening set, but his metronomic game eventually clicked and there was little Khachanov could do to top his opponent's march into the last four.
"He was the better player for most of the first two sets, I was struggling to find my rhythm, I came into this a bit sluggish," Djokovic said.
"Then I played a perfect tiebreak and from that moment onwards I played a couple of levels higher, managed to win eight points in a row to finish it off."
Djokovic was not completely happy with his performance but knew victory would not come easy.
"I missed a couple of easy shots today," he added. "These things happen sometimes it works, sometimes it doesn't."
"He has a big serve but maybe doesn't move as well so I tried to expose him and played unpredictable. It was a big fight but that's what you expect from a Grand Slam quarter-final."
Khachanov stole Djokovic's serve to lead 3-2 and, although the world number three threatened in a 10-minute ninth game, the Russian held and went on to pocket the set.
There were no break points in the second set but Khachanov started to struggle and paid for his efforts, failing to score a point in the tiebreak as Djokovic levelled the contest.
Djokovic got the early break thanks to a net-cord in the third and stole Khachanov's serve again to move one set from victory with apparent ease.
The Serbian broke again early in the fourth set, only to serve a double fault that allowed Khachanov to level for 4-4 and keep his slim hopes of an upset alive.
Coming back in the set cost Khachanov too much though and the Russian was broken to love in the following game, losing eight points in a row as Djokovic ended the contest with an ace.
Perfect tiebreak was the turning point
Djokovic's flawless second-set tiebreak proved the turning point in his victory over Khachanov but the Serb said he needed to improve if he is to book a spot in Sunday's final.
"It (tiebreak) was probably the turning point of the match," the Serb, chasing a record-breaking 23rd men's singles Grand Slam title, said.
"Winning the second set or, you know, losing the second set would be quite a big difference."
"It worked really well for me. I must say I played a perfect tiebreak, seven-love. Every point was perfectly scripted for me, so to say."
Djokovic, who is level on 22 majors with Rafael Nadal of Spain, had not dropped a set in his previous four rounds, but Khachanov had him on the ropes for almost two sets.
"Everything was going in a great direction and then I stepped out on the court today and probably part of me stayed in the locker room," Djokovic said. "That's how I felt, that's how I played."
"First couple sets, probably the worst two sets I played so far in the tournament. It's not the first match that I managed to turn things around. These kind of wins, I think serve as a great confidence booster mentally, so also physically and emotionally for me," he said.
"It's important to win a match where you were losing or you were being down and then you came back and won a match, especially at the latter stage of a Grand Slam," he said.
But he warned that he needs to up his game if he is to reach the final for a seventh time in Paris.
"I will analyse my game from today with my team, and be better prepared for the next one," Djokovic said. "Because I definitely need to have a better start in the semis."
