Captain Virat Kohli described Saturday’s 63-run win over South Africa in the third and final Test at the Wanderers as "a massive milestone" for Indian cricket.
"This is one of our sweetest wins," he said. "This day will be remembered for a long time for us as a team."
Kohli said India's performance on a pitch designed to help South Africa's fast bowlers showed they could win in any conditions.
"We already had the belief but now we have the result to back that as well."
He said belief in their own ability was crucial. "If we think about winning Test matches, yes, we will lose some but we will end up winning a lot as well."
Kohli added Saturday's win, achieved on the fourth afternoon after South Africa lost their last nine wickets for 53 runs, ranked as one of the finest he had been involved in as a player.
He compared it to a win under MS Dhoni’s captaincy against England at Lord’s in 2014.
"Lord’s was very special because we were playing on a similar sort of pitch," he said.
Asked whether he was concerned that South Africa were taking control during a second wicket stand of 119 between Dean Elgar and Hashim Amla, which took the hosts to within 117 runs of their victory target of 241, Kohli said: “I don’t think like people on the outside”, adding that he knew that if one wicket fell it could lead to a collapse on a difficult pitch.
The win entrenched India as the world's No 1 Test team. If South Africa had completed a 3-0 series sweep they would have drawn level on points with Kohli's men.
“South Africa played better than us in the first two games so they deserved to win [the series] but we deserved to win this game. But at many moments in the first two games we put them under pressure," Kohli added.
“We are the No 1 team in the world and we certainly played like that today.”
South Africa captain Faf du Plessis conceded that India had been the better team at the Wanderers but hailed the series win.
"It’s fantastic to win the series against a really good team. Credit to India for playing some really good cricket in all three Tests."
Du Plessis praised the effort of Elgar, who was struck on the helmet on Friday in an incident which led to the umpires and match referee deciding to call off play, leading to concerns that the match could become only the third Test ever to be abandoned.
Although conditions were difficult on Saturday there was none of the excessive bounce from a good length that there had been on Friday.
Elgar battled for almost six hours, facing 240 balls, to make 86 not out.
He became the first South African to carry his bat twice through a Test innings. "He’s our little bulldog," Du Plessis said.
Elgar said it was one of his toughest innings. "Personally it's an achievement but it's bittersweet because we want to win Test matches."
Du Plessis said he was disappointed about the quality of the pitch and said there needed to be discussions between team management and groundsmen about preparing pitches of a good standard.
"We never asked for anything excessive," he said. "Once again we are not getting it right."
Elgar and Amla battled until shortly before tea but then Ishant Sharma and Jasprit Bumrah sparked a dramatic collapse.
The hosts were looking comfortable as Elgar and Amla compiled a partnership of 119, although it took four hours and 50.4 overs of hard work. It was only the third century partnership of the series.
Ishant and Bumrah claimed two wickets each to start the slide before Mohammed Shami ripped through the lower order, taking 5-28.
Amla fell with the total on 124 when he clipped Ishant firmly towards midwicket and Hardik Pandya dived to his right to hold a good catch.
Amla had faced 140 balls in making his second half-century of the match.