The pair batted throughout the morning as South Africa reached 428 for three at lunch, still 201 runs behind England's first innings total of 629 for six declared, but with time running out for the tourists to force a result.
Amla was unbeaten on 200, while Du Plessis was on 81 not out.
Amla reached 200 shortly before lunch after batting for 682 minutes and facing 461 balls. He hit 27 fours.
But Joe Root at mid-on appeared to have difficulty picking up the flight of the ball, which dropped harmlessly nearby. The batsmen took two runs and Amla scampered a single off the next ball to reach his milestone.
It was slow going as England's bowlers toiled on an unresponsive pitch against batsmen determined to stay at the crease as long as possible.
Only 75 runs were scored in 30 overs during the morning.
Du Plessis, on 61, benefitted from England's fourth dropped catch of the innings when James Anderson at slip could not get his hands to an edged drive against off-spinner Moeen Ali.
With the pitch again offering no assistance to the bowlers, Anderson bowled only three overs during the morning.
Stuart Broad and Steven Finn sent down four each and Ben Stokes did not bowl at all. By contrast Ali bowled 12 overs on another hot morning.
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