Djokovic remains on court to grab injured Rafael Nadal's year-end No 1 ranking and he will now face the victor of the second semi-final between top seed and defending champion Roger Federer and highly-rated Croatian youngster Borna Coric.
Djokovic, this year's Wimbledon and US Open victor, will next face Germany's Alexander Zverev in the last four.
Edmund was bidding to reach his first Masters semi-final but a couple of forehand errors gifted Zverev a break in the opening game.
Zverev will next play second-seeded Djokovic in the semifinals.
Federer held off a late charge from the Japanese to take the opener before recovering from a 4-1 deficit in the second set tiebreak to seal victory.
The towering South Africa showed great athleticism to put away a backhand volley at the net and had a set point when Djokovic drilled a backhand wide, but the 14-time grand slam champion's serve got him out of a hole.
Díaz Canel es el primer presidente cubano con Twitter
Para su debut en esta red social, el gobernante cubano escogió el día en que los cubanos conmemoran el 150° aniversario del "Grito de Yara", que recuerda el inicio de la guerra de independencia contra el colonialismo español en 1868, en la finca " La Demajagua " (sureste).
The 37-year-old will next face Croatian power-hitter Borna Coric, who dumped Australia's Matthew Ebden out of the tournament 7-5 6-4.
"It was a different surface", Djokovic said of their previous match. "I think I can be very happy with my level of play this week".
Djokovic held the advantage to seal the victory and set up a semi-final clash with Germany's Alexander Zverev, who became the fifth singles player to qualify for November's ATP Finals with a 6-4 6-4 win over Kyle Edmund.
Djokovic did not give the world number eight a look-in, serving with power and precision and returning with vigour to remain in the hunt for a fourth title of the season.
The 21-year-old German made an iffy start, beginning his first service game with a double-fault.