Despite the swashbuckling effort from Smith (102 batting off 82 balls), England remain far away from India's 587 all out.
Smith smashed a memorable hundred in less than a session and Harry Brook (91 batting off 127) was on course to reach three figures at the break.
Strikingly, England hammered 172 runs in 27 overs in the first two hours of play.
Resuming the day at 77 for three, England lost half their side in the second over of the morning session when Siraj had Joe Root (22) and Ben Stokes (0) caught behind. Root's was a soft dismissal as he got faint tickle down the leg side while Stokes was surprised to get a sharply rising ball first up.
England were reduced to 84 for five but Smith and Brook continued to attack and put pressure back on the opposition.
Prasidh Krishna was brought in to implement the short ball plan with six fielders on the leg side but that failed as Smith got the better of him in the 12th over of the morning that yielded 23 runs. Four boundaries and a six over deep square leg came in that eventful over.
India persisted it with Krishna, whose following over went for 11. His figures after the session read 8-0-61-0.
It is not often that Brook is outscored but it happened on Friday as Smith relentlessly attacked the Indian bowlers.
Smith also did not allow spinners Ravindra Jadeja and Washginton Sundar get into any sort of rhythm. Sundar was driven for back-to-back fours by Smith in his first two balls before the wicket-keeper batter collected a six and a four from Jadeja in the following over.
Smith got to his second Test hundred off 80, the third fastest by Englishman, with consecutive fours off Jadeja in the last over before lunch.
Scoreboard at Lunch on Day 3 of the second Test between India and England here on Friday.
India 1st Innings: 587 all out in 151 overs.
England 1st Innings: (O/n) 77/3
Zak Crawley c Nair b Mohammed Siraj 19
Ben Duckett c Shubman Gill b Akash Deep 0
Ollie Pope c Rahul b Akash Deep 0
Joe Root c Pant b Mohammed Siraj 22
Harry Brook batting 91
Ben Stokes c Pant b Mohammed Siraj 0
Jamie Smith batting 102
Extras: (LB-4, NB-10, W-1) 15
Total: (For 5 wkts, 47 overs) 249
Fall of wkts: 1-13, 2-13, 3-25, 4-84, 5-84.
Bowling: Akash Deep 11-1-59-2, Mohammed Siraj 12-2-49-3, Prasidh Krishna 8-0-61-0, Nitish Kumar Reddy 1-0-1-0, Ravindra Jadeja 10-1-48-0, Washington Sundar 5-0-27-0.
