Left-arm spinner Jadeja and leg-spinner Chawla sent back Jonathan Trott and Ian Bell in the post-lunch period after Sharma had given India a rousing start in the morning session by dismissing openers Alastair Cook and Nick Compton cheaply.
Kevin Pietersen was unconquered on 68 after a stay of 193 minutes in which he hit nine fours along with debutant Joe Root (10) as England reached 133 for four at tea after the visitors won the toss and opted to bat.
The tourists, 61 for two at lunch, added 72 runs in 32 overs while losing Trott and Bell, in the second session.
For India, lone pacer Sharma was the most impressive of the lot and troubled the English batsmen with his aggressive bowling on a slow and low track. His tea figures were two for 25 in 14 overs.
Jadeja had figures one for 22 at tea while Chawla had one for 25.
First choice slow bowlers Pragyan Ojha, India's most successful bowler so far in the series, and Ravichandran Ashwin were wicket-less at the break.
Pietersen and Trott rallied England after the visitors' poor start when they were reduced to 16 for two by Sharma's twin strike in his first spell.