Set a world record victory target of 458, South Africa finished eight runs short on 450 for seven after a day of tension and drama.
"It was an unbelievable Test match," said Smith. "From day two we've been behind the game and I don't think many people gave us a chance to be in this position. As a team we showed real mental strength and the ability to handle pressure."
Du Plessis (134) and De Villiers (103) shared a fifth wicket partnership of 205 -- a world record for a fifth wicket stand in the fourth innings of a Test match.
For much of the day, a draw seemed to be the best result that South Africa could hope for, but with De Villiers in particular batting with positive intent, the required run rate was always below five runs an over.
With Indian captain Mahendra Singh Dhoni forced to set defensive fields, De Villiers was bowled with 56 runs required in 13.5 overs, attempting to run the ball down to third man but edging it into his stumps.
JP Duminy cracked a boundary off Mohammed Shami but was then bowled off an inside edge, attempting another drive.
Vernon Philander, who hit a half-century in the first innings, joined Du Plessis and pushed the score along while Du Plessis remained rock solid.
"When those wickets fell I decided I had to be there until the last four overs and then possibly have a go," said Du Plessis.
With 20 needed off four overs, Du Plessis pulled Zaheer Khan for four but was then run out by a direct hit from Ajinkya Rahane at mid-off as he attempted to retain the strike.
Du Plessis, who saved a Test with a century against Australia in similar circumstances on his debut in Adelaide last year, batted for 395 minutes, faced 309 balls and hit 15 fours.
"I thought about Adelaide quite a lot," he said. "Before that innings I didn't know that I could bat for four or five sessions. But the conditions here were tougher. The wicket was doing quite a lot more."
South Africa settled for the draw but Dale Steyn hit the last ball of the match from Shami for six to leave the hosts tantalisingly close.
Dhoni did not attend the post-match press conference but said at the presentation ceremony that his team would take confidence into the second and final Test in Durban.
"We needed a big effort from the quicks and they delivered. Our batting did extremely well too."
He said of the tense finish: "We might have been a little too attacking in the lead-up."
Virat Kohli, who was named man of the match after innings of 119 and 96, said he was surprised South Africa backed off going for the win in the closing overs.
There were some boos from spectators when it became obvious that the chase had been abandoned, which Smith said he could understand given the emotion of the occasion.
He said Philander and Steyn had made the decision after some short and wide bowling made scoring difficult in the two overs leading up to the final over.
"They were in the middle and I back their decision," he said.
Kohli gave credit to Du Plessis and De Villiers.
"They batted brilliantly. For Faf to bat under so much pressure showed a lot of character and we know AB is a world-class player."
Kohli said the Indian bowlers had performed well.
"We can't blame the bowlers, we must give credit to the batsmen," he said.
"We have a lot of young players and we can be really proud of the way we played in this Test match."
Du Plessis and De Villiers's partnership was launched after Khan claimed his 300th Test wicket when he won a leg before wicket decision against Jacques Kallis, South Africa's senior batsman.
Kallis, who made 34, look surprised when he was given out by umpire Rod Tucker.
Replays showed the ball had come off an inside edge. In a series in which the decision review system is not being used, it was the first major error made by umpires Tucker and Steve Davis.
Fast bowler Shami bowled Alviro Petersen in the fifth over of the day, after South Africa resumed at 138 for two, with Petersen failing to add to his overnight score of 76.
Once Kallis was out, there were still 74.2 overs remaining and India were favourites to close out victory, but Du Plessis continued to play an anchor role, while De Villiers played positively.
The world record for a successful run chase is 418 for seven by West Indies against Australia in St John's in 2002/03.
COMMENTS (4)
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It s not the fact of how much fast u bowl. It s matter of fact how technically bowling on that particular period. Is there any rules that ly akthar and johnson need to eyeballing the batsman. Even their overs also smashed by batsmans lot os times.
The funny thing was ishant sharma was bowling at 132 kph at best and eyeballing the batsmen as if he is mitchell johnson or shoaib akhter...lolzzz
Had it not been for the stupidest umpiring decision of giving Jacque Kallis out LBW on an inside edge, SA would have definitely won this epic encounter. Nevertheless, it was Test Cricket at its best.
The way S.Africa came back into this match and held on to a draw shows why they are number 1......... at the same time, their not going for the win shows why they can't win the big tournaments. Cricket is a game of technique, strategy and guts. They are missing the 3rd factor.