ATP Finals: Serbia's Djokovic breezes into final after straight-sets win
Anderson's best hope of victory was to dominate the Serbian star with his serve, but Djokovic struck a crucial early blow to the South African's confidence by breaking his serve in the very first game of the match.
From that moment on, Djokovic looked completely unruffled as he comfortably held serve without facing a single break and broke Anderson again in game seven to win the first set 6-2 in just 39 minutes.
The Serbian won his service game to love and Anderson gamely held serve to force Djokovic to serve his way to victory.
And the number-one seed did just that, winning the final game to love, with a cheeky net cord shot winning the game, the set and the match 6-2, 6-2 in just 75 minutes as he strolled into Sunday's final with consummate ease.
After the match, Djokovic said: "I think it was the best match that I've played this week and it came at the right time.
"Kevin has been playing some really good tennis this week. He lost the serve in his first game and that was a big difference."
Throughout the tournament Djokovic has dominated with his serve, which hasn't been broken all week. But he admitted he was surprised to have served more aces in the semi-final than his big-serving opponent.
"It is definitely not very common to serve more aces than Kevin, especially in my case, so that definitely helps."
Djokovic moves on to Sunday's final, where he will take on Germany's Alexander Zverev. The pair met in the round robin stages of the tournament where Djokovic ran out a straight-set victor, winning 6-4, 6-1.