India, kept in the field for over five sessions as South Africa piled up 540 in their first innings, hit back in style on a barren wicket that is proving to be a nightmare for bowlers.
Sehwag and Jaffer, who resumed at Thursday's total of 82-0, punished the tourists' attack by adding 94 runs from 25 overs in the morning session of the third day at the Chidambaram stadium.
Sehwag went to lunch on 110, his second successive century following a match-saving 151 in his last innings against Australia at Adelaide in January.
Jaffer, returning to the side after being dropped for the last two Tests in Australia, was unbeaten on 60.
Sehwag's 14th century in his 55th Test has so far contained 16 boundaries and a six -- an audacious slash over the slips against fast bowler Makhaya Ntini on Thursday evening.
The swashbuckling opener, India's lone triple century-maker in Tests, moved to 99 with a lofted on-drive off Jacques Kallis and reached his hundred with another skier over the bowler's head in the same over.
Jaffer was more circumspect, playing each ball on its merit as he moved towards his second consecutive hundred against South Africa after making 116 in Cape Town last year.
The South African bowlers struggled to contain the flow of runs as the batsmen cut, pulled and drove freely to the delight of 35,000 home fans.
Proteas captain Graeme Smith rotated his three fast bowlers, giving them 10 overs each. Dale Steyn conceded 42 runs, Ntini 48 and Morne Morkel 26 runs.
Left-arm spinner Paul Harris went for 28 runs in his 11 overs.