World Number One Djokovic broke Anderson known for his big serves twice in the first and once in the second set to wrap up the match in an one and 37 minutes.
Anderson who has two overall titles in the ATP tour including the one won last week at the Delray Beach had seven aces whereas Djokovic could deliver only five.
But Anderson’s win 41 percent win percentage in the second set worked against him.
Djokovic who incidentally lost the first time these two players met in 2008 now has four successive straight wins over the Six foot eight inch South African.
Djokovic will now meet Pablo Andujar of Spain who advanced into the fourth round after defeating his compatriot Albert Ramos.
Meanwhile in other matches played, John Isner of America cruised past Argentine Juan Monaco 7-5, 7-5 and French Gilles Simon defeated Stanilas Wawrinka of Switzerland 6-4, 6-4.
Apart from John Isner it was not a good day in house for the Americans with World Number 8 Mardy Fish and former World number 1 Andy Roddick being knocked out of the tournament. Mardy Fish lost 6-3, 6-4 to the qualifier Matthew Ebden of Australia whereas Roddick lost to World number 7 Tomas Berdych 6-3, 4-6, 6-2.
By Indian Sports News Network