Opening batsman Amla weighed in with 55 off 58 balls, while Duminy was not out on 66 off 87 deliveries. South Africa, chasing Sri Lanka's 236 for six, reached 237 for five with eight balls remaining.
Amla and Graeme Smith (28) provided the hosts with an impressive start thanks to an opening stand of 76 before Duminy controlled the middle-order as the hosts took a 2-0 lead in the five-match series.
Amla looked in complete control during his innings, which included five fours and two sixes. Duminy was content to simply work the ball around and struck just one six.
Sri Lanka owed their final total to Dinesh Chandimal, who ended not out on 92, and left-handed opening batsman Upul Tharanga. He made 66 off 85 deliveries with six fours and a six.
Chandimal, together with Nuwan Kulasekara (22) and Angelo Mathews (28), provided the innings with some late impetus.
The third match of the series is in Bloemfontein on Tuesday. South Africa won the first game by 258 runs.
