Top seed and 2016 champion Djokovic won 6-4, 6-3, 6-3 against Russian 15th seed Khachanov to draw level with Rafael Nadal on a record 14 quarter-final appearances in Paris
World number two Nadal, the highest seed left in the draw after the early ouster of No. 1 Novak Djokovic, dominated both tiebreakers to beat the towering Russian 7-6 (7/2), 7-6 (7/2).
Djokovic's record in Doha is now 13 wins and just one defeat and his path to a potential third title in four years.
In their 47th career head-to-head on Saturday, the Serbian moved to one win away from his fifth title at the tournament after triumphing 7-6 (6), 5-7, 7-6 (3) in over three hours to improve the record to 25-22
The top seeded Spaniard triumphed after an epic 4 hour 23 minute struggle on Arthur Ashe Stadium in a match where the 22-year-old Khachanov had served for a two sets to love lead in the 10th game of the second set and had a set point in the fourth-set tiebreaker.
Roger Federer, chasing a ninth title at the Halle grass court tournament, despatched Russian Karen Khachanov 6-4, 7-6 (7-5) on Saturday to move into the final.