Seeking to complete a 5-0 series sweep, South Africa scored 384 for six after being sent in to bat.
De Kock hit 109 off 87 balls, playing the dominant role in an opening partnership of 187, a record for South Africa against Sri Lanka.
Amla was more circumspect initially but went on to make 154 off 134 balls.
It was Amla's 24th one-day international century, equalling captain AB de Villiers' South African record, but he survived chances on 27 and 42 as Sri Lanka, nearing the end of a largely dispiriting tour, gave a mediocre fielding performance.
De Kock needed only 80 balls to reach his 12th hundred in just 74 one-day internationals. On the ground where he hit 178 against Australia in his previous one-day appearance, another big score seemed possible as he reached his century in the 25th over but he only faced seven more balls before he was caught on the point boundary.
Most of the bowlers took heavy punishment but Suranga Lakmal claimed three wickets while conceding 71 runs in ten overs.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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