During the match against South Africa, Saha proved exactly what he is capable of as he grabbed a stunning piece of a one-handed catch, diving to his left to send de Bryun packing at the best scene.
The comprehensive victory, coming on the fourth day, has consolidated India's top position in the World Test Championship table.
Captain Faf du Plessis, promoting himself to No.4 this time around, stuck in for a gritty 5 off 54 balls, but when he, opener Dean Elgar, and Quinton de Kock all fell in the space of five overs, a quick finish looked on the cards.
Temba Bavuma and Quinton de Kock were the next batsmen but the latter was bowled by Ravindra Jadeja, putting the host under vast pressure.
Vernon Philander and Keshav Maharaj, who combined for 109 in the first innings, added 56 for the eighth wicket to delay India's win before Yadav finally broke the stand when Philander edged one down the leg side to be out for 37.
However, Umesh Yadav came out furiously in the 67th over and took two wickets.
"In the last three to four years it's awesome to see the hunger in this group to keep improving".
"As a captain you are trying to think of ways, how you can change little field placements, bowlers but he was too good", Du Plessis said of Kohli.
"He's taken that risk, which a lot of other captains have not been able to take". "Virat has a mindset of winning test matches either at home or overseas!" "The hunger stood out, it was great value for us as batters".
The Proteas were dismissed for 275 at the end of day three in Pune after India's 601-5 declared, 127 short of the follow-on.
Ravindra Jadeja (3/52), Ravichandran Ashwin (2/45), Mohammed Shami (1/34) and Ishant Sharma (1/17) played their part in the comprehensive victory.
MATCH REFEREE: R.B. Richardson (West Indies). "We saw that in the first Test as well", added Du Plessis, whose side were crushed by 203 runs in the series opener in Visakhapatnam last week.