Kohli century keeps India in touch with South Africa
Virat Kohli received minimal support from his team-mates, with Murali Vijay (46) and Ravichandran Ashwin (38) the only other batsmen to reach 20.
Ashwin helped Kohli add 71 off 87 balls for the seventh wicket but he lived dangerously after being peppered by short-pitched balls from Kagiso Rabada at the start of his innings.
South Africa's second innings got off to a poor start as Bumrah reduced them to three for two.
Aiden Markram was Bumrah's first victim, falling leg before wicket as he played back to a ball which cut back and kept low. Bumrah followed up with the wicket of Hashim Amla, who was also trapped on the back foot by a similar delivery.
Both batsmen were so palpably in front of their stumps that neither sought a review.
India had opened the bowling with off-spinner Ashwin and he troubled left-handed opener Dean Elgar. But Elgar survived to share an unbroken 87-run partnership with AB de Villiers, who batted confidently to reach 50 not out. Elgar was unbeaten on 36.
A thunderstorm interrupted play for an hour when South Africa were 68 for two. It resumed for another 27 minutes under gloomy skies with the floodlights on before bad light ended the day.
Both batsmen survived some anxious moments, in particular Elgar, who on 29 edged Bumrah at catchable height between wicketkeeper Parthiv Patel and first slip Pujara.