Playing one of the slowest innings in Test history, Amla scored 25 painstaking runs off 244 balls. He took 46 balls to open his account. De Villiers took 32 balls to get off the mark.
India ended South Africa's second innings at 143 runs to win the fourth and final cricket Test by 337 runs and clinch the series 3-0 at the Ferozeshah Kotla here on Monday.
This was the first series victory at home for Indian skipper Virat Kohli and his second consecutive one after the triumph in Sri Lanka in September.
India had won the first Test in Mohali and the third in Nagpur earlier in this series. With the series-win, India climbed to the second position in the International Cricket Council (ICC) Test rankings.
Off-spinner Ravichandran Ashwin was the most successful among the Indian bowlers in the second innings with figures of 5/61.
Fast bowler Umesh Yadav bagged three quick wickets just after tea to return figures of 3/9. Left-arm spinner Ravindra Jadeja returned with 2/26.
Jadeja bowled 17 consecutive maiden overs in the second innings. He fell four maiden overs short of the existing record of former India spinner Bapu Nadkarni when Faf du Plesis walloped him to the long-on boundary.
A.B. de Villiers was the highest scorer for the visitors with 43. De Villiers consumed 296 deliveries during his marathon innings.
Usually known and revered for his ability to repeatedly hit bowlers out of the park in limited-overs cricket, the 31-year-old showed he is one of best when it comes to defensive batting as well.
Although Hashim Amla, du Plessis and J.P. Duminy fell at the other end, the experienced right-hander continued to hold back the Indian bowlers at the other end.
His lengthy partnerships with Amla and du Plessis gave the Proteas genuine hopes of snatching a draw before they suffered a dramatic collapse shortly after the tea break.
Resuming at the overnight score of 72/2, South Africa batsmen de Villiers and Amla continued their efforts to deny a victory to the hosts.
Du Plessis took 53 deliveries to open his account. He is now third on the list of batsmen consuming most number of balls before opening their account.
England's John Murray (80 deliveries) holds the record in this dubious category which came against Australia in the Ashes series of 1962.
England's Stuart Broad is second on the list with 62 balls which came against New Zealand in 2013. Grant Flower of Zimbabwe is fourth with 51 balls. He achieved the feat in the year 2000 against New Zealand.
Jadeja knocked back Amla's off-stump in the morning session before du Plesis joined de Villiers in the middle and the duo ensured that the visitors did not lose any more wickets till lunch.
Amla scored 25 runs off 244 deliveries. The elegant right-hander has not been at his best in this series. But he played a captain's innings when his team needed it the most and it needed a superb delivery from Jadeja to dislodge him.
The Kotla pitch became slow as the Test match progressed and lost most of its bounce which allowed the visitors more time to read the deliveries and play their shots.
Kohli used eight bowlers, including himself, in an attempt to dislodge the Proteas batsmen.
Jadeja struck another big blow to South African hopes when he trapped du Plessis leg before almost immediately after lunch with one that kept straight after pitching.
Ashwin sent Duminy back to the pavilion before the South African had opened his account to revive Indian hopes just before tea.
The Proteas hopes of avoiding defeat vaporised right at the start of the final session when they lost their last five wickets in the space of seven runs.
Dane Vilas was a bit unlucky when he was slightly late in bringing his bat down to an off-cutter from Yadav that moved sharply in from outside the off-stump. The ball took the edge of the bat before hitting the stumps.
Ashwin finally ended de Villiers' marathon vigil in the very first ball of the next over when the South African was surprised by the extra bounce and was caught by Jadeja at leg slip.
An Indian victory was only a matter of time after that.
Yadav dismissed Kyle Abbott and Dane Piedt in quick succession before Ashwin bowled Morkel to send his team-mates and the crowd into raptures.