Buttler scored 89 and put on 98 with Stuart Broad for the ninth wicket as the home side recovered from 198-7 after day one to 332 all out.
India then slumped to 174-6 in reply. Anderson took two quick wickets as the tourists faltered from 101-2 to 103-4, before Stokes matched him, his two victims including India's captain and kingpin Virat Kohli for 49.
He also removed Rishabh Pant late on, Alastair Cook, playing in his final test, pouching the edge for his 13th catch of the series, an England record.
England have already built up an unassailable 3-1 lead in the series after victory in Southampton last week.
Anderson made the key breakthroughs after tea, grabbing the wicket of the well-set Cheteshwar Pujara, the hero of India's first innings in the fourth test, and then following that up with the wicket of vice-captain Ajinkya Rahane.
Kohli, however, who has had a prolific tour, was scoring at a healthy rate and was nearing his half-century when all-rounder Stokes induced him to edge to second slip in a rare lapse of concentration.
England's fightback had been launched by Buttler in the morning.
Jasprit Bumrah struck early for India by trapping Adil Rashid lbw to leave the hosts tottering on 214-8.
Broad, however, grafted his way to 38 to thwart the visitors during his partnership with Buttler which ended when the fast bowler, having batted more than an hour and a half, was finally dismissed by Ravindra Jadeja to make it 312-9.
Broad played and missed numerous times, with Mohammed Shami and Jasprit Bumrah getting the ball to swing in chilly and slightly overcast conditions, before he fell to a brilliant diving catch by Lokesh Rahul at long on.
Buttler, England's most successful batsman of the summer, was happy to milk the bowling for singles while also striking some lovely shots on either side of the wicket, including six boundaries and two sixes before he was the last man out.
(Reporting by Saikat Chatterjee; Editing by Tony Lawrence)
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