Proteas were scoring after they were put into bat was hit badly due to the untimely break due to rain in the 42nd over.
However, India need 268 to win in 46 overs under Duckworth-Lewis rule and clinch the series.
Amla once again proved to be India's nemesis as he scored another century to guide South Africa to a decent total at the Supersport Park in Centurion.
The Indian pace duo of Munaf Patel (3/50) and Zaheer Khan (2/47) regrouped well to bowl an immaculate line at the death after the match was reduced to a 46-over-a-side affair due to a rain interruption.
From 226 for three in 42 overs at the rain break, South Africa lost six wickets to end their innings at 250 for nine.
It was Amla's seventh ODI century in his 42nd appearance. Interestingly, Amla started the Test series before the one-dayers with a century and has now finished the ODI series with a three figure mark -- both at the same venue.
Amla's century came off 113 deliveries with nine boundaries. The highlight of his innings was the number of singles and twos he ran. His century came when he played a delicate late cut of a Suresh Raina delivery to guide the ball to third man boundary.
The only glitch in an otherwise flawless innings was the reprieve he got when he was batting on 70. Amla hit a pull shot as part-time off-spinner Rohit Sharma dropped one short. The catch that flew towards square leg was dropped by 12th man Ravichandran Ashwin.
The foundation of the South African innings were the two solid partnership - the first one being a 97-run stand between Amla and Morne Van Wyk (56 from 63 balls) who put on 97 runs for the second wicket in 19.5 overs.
The second one was between Amla and Jean-Paul Duminy (35 from 44 balls) who added 102 for the fourth wicket before Duminy perished trying to hit Munaf Patel over mid-wicket.
Earlier, Indian captain Mahendra Singh Dhoni elected to field on a wicket which didn't have much for the seamers. Piyush Chawla was drafted in the playing XI in place of Ashish Nehra.
The choice was understandable considering this will be the only chance when the team management were able to have a good look at Chawla ahead of the World Cup.
The Indians started off well with senior pro Zaheer Khan again getting his 'bunny' Graeme Smith (7) as the Proteas captain fished at a delivery outside the off-stump and was smartly caught by Yusuf Pathan stationed at second slip.
But number three batsman Van Wyk provided good support to Amla who punished the loose deliveries but at the same time ran the singles and twos well.
With the surface being on the slower side, Dhoni used six slow bowlers. Chawla, who has been a surprise inclusion in the World Cup squad, didn't impress. He wasn't exactly taken to the cleaners by Amla-Van Wyk pair, but the leggie could do precious little to stop the singles which the South African duo got easily.
Apart from Yuvraj Singh (2/45), who again impressed with his slow left-arm orthodox bowling, none of the other slow bowlers were able to make any sort of impact. Amla in particular ensured that the run rate never dropped below five per over mark.
It was a brilliant reflex catch by Yuvraj that saw the end of Van Wyk just after he had scored his third half century in ODIs.
Yuvraj also foxed AB de Villiers (11) with a ball that spun sufficiently to beat the batsman's willow as keeper Dhoni whipped the bails in a flash. From 113 for one, the hosts were 129 for three in no time.
However, Amla and Duminy averted any further danger although the latter survived a confident leg before appeal from an arm-ball bowled by Yuvraj. The television replays showed that the ball would have gone on to hit the leg-middle.