Medium pacer Nabi picked five for 26 while spinner Tiwary grabbed three for 12.
At stumps, the hosts were 51 for one in their second knock, stretching their overall lead to 273.
The batsman to be dismissed was Shikhar Dhawan (18) while F Y Fazal (14) and captain A T Rayudu (19) were at the crease at stumps.
Earlier A Miller (4-76) and T C Smith (3-35) gave England a bright start as India, resuming at 311 for six, folded for 334 in 102.4 overs.
But the tourists lost the initiative with none of the batsmen standing up to the challenge of home bowlers.
Only J L Denly (59) and M O'Shea (20) produce semblence of a fight.