India was earlier bowled out for 365 before lunch and got a lead of 160 runs. No. 8 batsman Washington Sundar was left stranded on 96 not out after India lost the last three wickets within five balls after it resumed on 294-7.
Left-arm spinner Patel, who grabbed 11 wickets in the last test at the same venue in India’s 10-wicket win within two days, finished the game with yet another impressive haul of nine wickets in his hometown.
India recovered well to clinch the series after losing the opening test at Chennai.
The world test championship final is at Lord’s in June.