The second seed ploughed through the first set, finding himself 5-0 up before the South African found a foothold. Djokovic went on to take the set 6-2.
Anderson held things equal in the second set until he lost the seventh game, after which he never recovered. The match ended 6-3 6-4 6-2.
The Serb will now go on to play either Cypriot Marcos Baghdatis or Italy’s Andreas Seppi.