India face a revised target of 268 off 46 overs using the Duckworth Lewis method.
Amla scored his seventh ODI hundred and shared substantial partnerships with Morne van Wyk (97 runs off 120 balls) for the second wicket and 102 off 101 balls with JP Duminy for the fifth-wicket stand.
Winning the toss and putting South Africa into bat, India hoped to capitalise on the movement in the wicket in the early part of the day.
Captain Mahendra Singh Dhoni also risked replacing one of his seamers, Ashish Nehra, with leg spinner Piyush Chawla, who last played a one-day game in the 2008 Asia Cup and, for the first time in the series, India went in with only two seamers - Zaheer Khan and Munaf Patel - and two specialist spinners in Chawla and Harbhajan Singh.
South Africa though did not pick their leg spinner Imran Tahir, and remained unchanged from the team which beat India by 48 runs, using the Duckworth Lewis calculation, in the rain-affected ODI in Port Elizabeth on Friday night.
It was the seamer, though, who made the breakthrough as Khan got his man early.
Graeme Smith (7) got a healthy edge to the slips, where Yusuf Pathan standing at second slip poached the catch from Rohit Sharma at first slip.
It was the fifth time out of nine ODI meetings where Khan has taken Smith's wicket, and he has also dismissed Smith six times in the same number of Tests.
The next two wickets went to part-time bowler Yuvraj Singh who reached out with his left hand and caught Van Wyk off his own bowling after Van Wyk had scored his third ODI half-century, making 56 off 63 balls including eight fours.
AB de Villers (11), fooled by the flight of the ball, ran down the wicket and watched the ball turn past him. He was stumped by Dhoni off Yuvraj in similar fashion to his last innings at St George's Park, although his previous wicket was recorded as caught behind.
At the rain break, South Africa were looking good at 226/3 off 42 overs, but Duminy (35) fell to Munaf Patel in the first over after the interruption when Patel took a comfortable catch off his own bowling.
In the next four overs, South Africa lost six wickets for 26 runs, with the last three wickets falling on 250.
Munaf Patel ended with 3/50 while Khan took 2/47.
India require 268 for victory.
ScorecardG.Smith c Pathan b Khan 7
H.Amla not out 116
M.van Wyk c and b Yuvraj Singh 56
A.de Villiers st Dhoni b Yuvraj Singh 11
J.Duminy c and b Patel 35
F.du Plessis b Patel 8
J.Botha c Dhoni b Patel 2
R.Peterson b Khan 4
D.Steyn run out (Dhoni) 0
M.Morkel run out (Dhoni) 0
L.Tsotsobe not out 0
Extras (lb6, w5) 11
Total (9 wkts, 46 overs) 250
Fall of wickets: 1-16 (Smith), 2-113 (Van Wyk), 3-129 (De Villiers), 4-231 (Duminy), 5-242 (Du Plessis), 6-244 (Botha), 7-250 (Peterson), 8-250 (Steyn), 9-250 (Morkel)
Bowling: Khan 9-1-47-2 (w2), Patel 8-0-50-3, Chawla 7-0-32-0, Harbhajan Singh 8-0-33-0, Pathan 2-0-10-0 (w1), Yuvraj Singh 8-0-45-2 (w1), Sharma 2-0-14-0, Raina 2-0-13-0 (w1)
Did not bat: L. Tsotsobe
India: MS Dhoni (capt), Parthiv Patel, Rohit Sharma, Virat Kohli, Yuvraj Singh, Suresh Raina, Yusuf Pathan, Piyush Chawla, Harbhajan Singh, Zaheer Khan, Munaf Patel
Match situation: India need 268 to win (Duckworth/Lewis method)
Toss: India
Umpires: Brian Jerling (RSA), Simon Taufel (AUS)
TV umpire: Shaun George (RSA)
Match referee: Chris Broad (ENG)