England, leading the five-match series 1-0, finished the day at 67-1, with opener Ben Duckett dismissed for 28 in Visakhapatnam.
Duckett and Zak Crawley put on an aggressive 50-run partnership before Ravichandran Ashwin claimed his 497th Test wicket by dismissing Duckett.
Nightwatchman Rehan Ahmed, at nine, joined Crawley with England needing another 332 for victory.
The highest successful fourth-innings target chased against India is England’s 378 at Edgbaston in 2022, while the most successful chase in India was the hosts getting 387 against England in 2008.
Spinners Tom Hartley and Ahmed combined to bowl out India for 255 after Gill’s 104 on a day of exceptional bowling and fielding.
James Anderson removed the openers early, and a stunning catch by captain Ben Stokes further set back India before Gill stabilized the innings.
Gill, scoring his third Test ton and first in 12 innings since March 2023, rescued India from 122-4 with two crucial stands, including an 89-run partnership with Axar Patel.
Despite a couple of fortunate escapes, Gill batted fluently with flicks and drives until he was caught behind attempting a reverse sweep off debutant spinner Shoaib Bashir.
England continued to make inroads, with Hartley dismissing Axar lbw for 45 before Ahmed took down Ashwin to wrap up the innings with his third wicket.
In the first session, Shreyas Iyer made 29 but was brilliantly caught by Stokes after attempting a big hit off Hartley. Anderson’s excellent morning spell also saw him rattling Rohit Sharma‘s stumps and getting Yashasvi Jaiswal caught at first slip for his 695th Test wicket.
Starting their second innings with a lead of 143, India began the day on 28-0.
