Washington and Axar played out the first hour on day three without much fuss to extend India's lead to close to 150.
Axar was run out for 43 after making 106 for the eighth wicket with Washington.
Washington was left stranded on 96 as India lost three wickets in four balls.
Stokes picked four wickets as India posted 365 and took a 160-run lead.
Ashwin dismissed Crawley and Bairstow on consecutive balls after lunch to push England to 10 for 2.
Sibley and Stokes fell to Axar in quick succession to leave England reeling.
Ashwin and Axar picked up three each in the second session to reduce England to 91 for 6 at tea.
Axar picked up his fourth five-wicket haul after dismissing Foakes and Bess in quick succession.
Ashwin picked up a five-wicket haul as well to help India seal a win by an innings and 25 runs. They also sealed a berth in the World Test Championship final.