The hosts wrapped up the three-match series with a 282-run victory in the second Test in Cape Town, and they are well on course for a series whitewash having finished day one of the final Test on 338-3.
Amla stole the headlines with a spectacular and timely return to form, marking his landmark 100th Test appearance by reaching triple figures for the first time in his last 13 innings.
The 33-year-old becomes just the eighth player to score a century in their 100th Test, eventually ending the day on 125 not out alongside the scoreless Duanne Olivier at the crease.
Most of Amla's time in the middle was spent with Duminy (155), though, as the pair put on a mammoth partnership to take control of the match.
However, they will go into day two in a strong position as they look to wrap up a 3-0 series win.