The hosts piled up 8-564 before declaring their first innings and unleashing their spin-heavy attack on Afghanistan.
Left-arm tweaker Suthar claimed 6-33 as India bundled out Afghanistan for 152 in the first innings before enforcing the follow-on.
Indian off-spinner Washington Sundar (4-36) did most of the damage in Afghanistan's second innings as the visitors folded for 112 on Monday. Sharafuddin Ashraf did not bat with a quad injury.
Earlier, Afghanistan lost their last five wickets in the morning session of the third day, after resuming their first innings on 5-113.
Rahmat Shah (60) led their resistance in the first innings with a composed knock that included nine fours and a six.
Suthar, who had already removed Ashraf caught behind, bowled Rahmat round his legs to complete a five-wicket haul. He then sent back Mohammad Saleem in the same over.
Afghanistan wilted after barely crossing the 150 mark but their openers had to walk out to bat again after India captain Shubman Gill enforced the follow-on.
Seamer Mohammed Siraj trapped opener Abdul Malik for eight but Sediqullah Atal (42) and Rahmanullah Gurbaz (24) decided to counter-attack.
Kuldeep Yadav (3-30) cut short Gurbaz's run-a-ball knock and Rahmat (13) also threw away his wicket trying to go after spinner Sundar.
Yadav removed Nangeyalia Kharote and Saleem off successive deliveries to seal India's victory on a frenetic day when 14 Afghan wickets tumbled.
Suthat took one second innings wicket, finishing with 7-62 for the match.
