The world number one fought back from a 0-3 deficit in the first set to come through the contest 6-4 6-3.
"It's a great step forward for me," Djokovic is quoted as saying by Eurosport.
"I did not have the feeling that the ankle was bothering me, I was very solid. I elevated the level of my game in the past two matches, definitely."
Djokovic will meet Italy's Fabio Fognini for a place in Sunday's final.