Trott (143) and Bell (87 not out) took their stand to 208 as England reached a teatime 310 for four, and lead of 314, and India's hopes of a last-ditch chase to salvage a 2-2 scoreline receded to nil.
It is almost 28 years since England won a Test series here, under David Gower and when current captain Alastair Cook was a babe in arms only weeks old.
England's number three reached three figures with a trademark boundary wide of mid-on off leg-spinner Piyush Chawla, and celebrated with feeling amid Indian faces resigned to a first home series defeat in eight years.
Bell, by his own admission, has not done himself justice in three Test tours to this country but made no mistake this time in a fine supporting role on his way to and beyond a 130-ball half-century.
There was barely a moment's anxiety as he and Trott continued Sunday's good work, having joined forces at a wobbly 94 for three when Kevin Pietersen was bowled shouldering arms at Ravindra Jadeja on Sunday night.
Trott's only alarm came shortly before lunch when he missed a Chawla top-spinner and was hit on the back pad, but umpire Rod Tucker turned down the lbw appeal - ensuring a wicketless morning session.
Bell did nothing to lighten their mood either, bringing up the 200 stand for the fourth wicket by hitting Jadeja for six over long-off and nearing a century himself - having had just one escape on 75 when a fierce cut at Chawla was edged and put down by Virender Sehwag at slip.
Trott finally fell soon afterwards, caught at leg-slip off Ravichandran Ashwin to the 310th ball he faced.