World number one Djokovic, chasing a sixth Wimbledon and record-equalling 20th Grand Slam title, won 6-3, 6-3, 6-3 over the 102nd-ranked South African.
However, he slipped and fell on at least five occasions on Centre Court, the day after Serena Williams suffered a tearful, tournament-ending injury on Tuesday due to similar slips.
Each time, 34-year-old Djokovic dusted himself down to set up a clash against either Italian veteran Andreas Seppi or American qualifier Denis Kudla.
Despite the tumbles, the Serb cruised to victory over the man he defeated in the 2018 final without facing a single break point and committing just six unforced errors.
2011: ✅2015: ✅2018: ✅2021: ✅History repeats itself for @DjokerNole as the defending champion beats Kevin Ander… https://t.co/oBTZdUAgbs
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“I have a nice connection with the crowd,” said Djokovic.
“I also seem to be having a really nice connection with the grass. I don’t recall falling so much in the first two matches at Wimbledon previously.”