At lunch, Cheteshwar Pujara and skipper Virat Kohli were batting at 20 and 4 respectively while Archer was 2 for 25.
Pacer Joffra Archer strengthened England's position by removing both openers, while India responded with 57 578 for the hosts' first innings in the opening Test on 2 February.
At noon, Cheteshwar Pujara and skipper Virat Kohli were batting at 20 and 4 respectively while Archer's wicket was 2 for 25. The home team initially lost opener Rohit Sharma (6), while Jose Butler's side lost a wicket after Archer got the ball to move the shed. With extra bounce.
India suffered another setback when youngster Shubman Gill (29, 28 balls, 5 fours) got a superb catch by veteran James Anderson at mid-on when the on-drive failed to continue.
Earlier, England recorded 57,578 in their first innings, losing the last two wickets in the morning session while adding ૨ runs to the overnight score.
Dom Base (34, 105 balls, 6 fours) was the first to go, before Jaspreet Bumrah hit the ball.
No. 10 Jack Leach (unbeaten 14) and No.1 James Anderson (1) extended England's innings further by five overs before being bowled when Ravichandran Ashwin failed to connect the slog-sweep.
Ashwin, who has bowled the most 55 overs in 1 innings so far, was quick with 166 runs for his efforts while Bumrah was also quick with three wickets for 84 runs in 36 overs. Ishant Sharma (2/52) and Shahbaz Nadeem (2/167) were two wickets quick.
Skipper Joe Root's marathon innings of 218, after winning the toss and choosing to bat, was the basis of England's huge total on the dile il pitch.
Openers Dominic Sibili (87) and Ben Stokes (8) were the other main contributors.
England finished with 555 for eight, while Root led the way with a marathon effort of 218 (balls 37 balls, 19 fours, 2 sixes) and two big partnerships with Sibley and Stokes.
Root also became the first cricketer to score a double century in his 100th Test.
Scoreboard at noon on the third day of the opening test:
England 1st Innings: 578 All Out
India's first innings: Rohit Sharma C Butler B Archer 6 Shubman Gill C Anderson B Archer 29 Cheteshwar Pujara 20 Virat Kohli Batting 4
Extras (B-0, LB-0, W-0, NB-0) 0
Total (2 wickets, 14 overs) 59
Fall of wickets: 19-1, 44-2 James Anderson 4-0-17-0, Joffra Archer 5-0-25-2, Ben Stokes 3-1-9-0, Jack Leach 1-0-6-0, Dominic Base 1-0-2-0.