The first three wickets fell for eight runs as they slipped to 3-216 with Root's misfortune accompanied by a full-house "send-off" from his opposite number Virat Kohli.
Former England captain Michael Vaughan told BBC Test Match Special: "Alastair Cook will be gutted to get out, but the man whose head will be down in England's dressing room is Dawid Malan".
Jennings left after the lunch break scoring 42 runs.
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Just as the partnership was starting to look ominous, left-arm swing bowler Sam Curran dismissed Pandya with a brilliant yorker. After England, Australia have played the most Test matches (812), followed by West Indies (535), India (523), South Africa (427), New Zealand (426), Pakistan (415), Sri Lanka (274), Bangladesh (108), Zimbabwe (105).
Root looked on course for his first hundred at this level since he made 136 against West Indies in last year's day/night Test at Edgbaston.
The hosts, playing their 1000th test, had lost six wickets for 67 runs as they limped to the close on 285 for nine on Wednesday.
Jennings had earlier helped Root put on 72 for the second wicket, but was long back in the pavilion by the time the captain was short of his ground answering Bairstow's improbable call for a second run to midwicket. From a position of security, however, the India unraveled in a hurry with Curran, in his just his second Test match, taking three wickets in one spell.
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It may have taken Broad a while to get Rahane, an average of 46.3 balls per wicket, but he still picked him up cheaply - twice caught by keeper Matt Prior and a screamer at third slip by Gary Balance in the fifth test.
Post lunch, Stokes (2-40) took two wickets in the space of five balls as India's middle order was completely rocked.
It was nearly an easy-going partnership for the opening duo as they brought up 50 off just 70 balls before the drama began.
But first-change Curran made it 50 for one in the 14th over when Vijay was lbw on review after missing a well-pitched-up inswinger.
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After Cook's dismissal there were few alarms for the England batsmen although Mohammed Shami continued to look unsafe for India - beating Jennings with a beauty in the 21st over.