The hosts piled up 564-8 before declaring their first innings and unleashing their spin-heavy attack on Afghanistan.
Left-arm spinner 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. Sharafuddin Ashraf did not bat with a quad injury.
"A complete win from our side, ticked all the boxes, so very happy," India captain Shubman Gill said after the win.
"It was very hot. We decided that if we bowl them out by lunch or around the first drinks break in the second innings we will ask them to bat again," Gill said of his decision to enforce the follow-on.
"For the spinners it was more about getting the experience of how to set up the batters."
Earlier, Afghanistan lost their last five wickets in the morning session of the third day itself after resuming their first innings on 113-5.
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 the legs to complete a five-wicket haul. He also 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 decided to enforce 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 - both batters fell to rash strokes - to seal India's victory on a frenetic day when 14 Afghan wickets tumbled.