Yorkshire’s Joe Root began day four by underlining his reputation as the side’s middle-order maestro, turning his overnight 118 into 182 not out, the latest in a line of ‘daddy hundreds’.
That helped England to 464, and a healthy first-innings lead of 165, but their prospects receded as the hosts reached stumps 37 ahead on 202-2.
All Alastair Cook’s side had to show for 75 overs of hard labour on a flat deck were the wickets of Devon Smith (2) and Darren Bravo (69), with Brathwaite bedding down for 101 not out in 230 balls.
Barely a ball seamed all day, with no obvious deterioration, bringing memories of the series-opening draw in Antigua flooding back.
England managed just five of the eight required wickets on day five there, and face an even steeper task at the National Stadium.
There was also precious little spin, though Moeen Ali was rusty after being rushed back into the side and never looked like getting into the game.
Yorkshire batsman Root was at his effortless best in the morning, scoring 64 runs from the same number of deliveries in fashion.
Despite his boyish visage, Root is developing into one of the sport’s most ruthless operators.
Of his six Test hundreds, one was converted into a double, three others have exceeded 150 and another saw him stranded on 149 not out.
The 24-year-old passed 2,000 Test runs in the process yesterday, making him the second youngest Englishman to do so after captain Alastair Cook and the ninth quickest in innings played.
He ensured the game moved along briskly, with 91 runs and four wickets to wrap up the innings.
Root looked as though he would never get out, clattering Devendra Bishoo for two steepling sixes, whipping length balls into the on-side at will and managing the strike expertly with the tail.
But his skilful showing was not matched elsewhere. His overnight partner Jos Buttler under-delivered on high hopes, successfully charging Bishoo to reach 13 only to be stumped attempting an action replay.
Chris Jordan was lucky to survive when an inside edge off Shannon Gabriel hit off stump only for the bails to remain unmoved.
He was run out for 16 after numerous replays confirmed Jason Holder’s flat return had beaten him back, while Broad unsuccessfully reviewed a gloved catch and fell for a duck.
That left England 431-9, but Root batted brilliantly with Anderson to add 33 for the 10th wicket.
But he was left high, dry and visibly angry when Anderson was stupidly run out, apparently unaware that Holder had gathered a wayward throw and was in the process of parting the stumps.
It was a harebrained moment but Anderson was soon back in the good books when he took the first West Indian wicket in his second over.
His first nine deliveries with the new ball were seen off by Brathwaite, but it took just one to remove the left-handed batsman Smith.
The Grenadian made a mess of both judgment and execution, unsure whether to play or leave and settling for a messy drag on.
That sent England to the lunch break in good heart, but their spirits ebbed in a wicketless afternoon session.
Brathwaite and Bravo put on exactly 100 runs between lunch and tea with scarcely a moment of concern.
Ben Stokes was milked for 27 in a costly four-over spell that included six boundaries for the West Indies.
Brathwaite took a particular liking to the all-rounder, sending his first two deliveries to the ropes and flashing two more thick edges between slips and gully.
Bravo also punished Stokes when he offered width, bringing an early end to the spell.
Both batsmen reached fifty with fours behind square, an endlessly profitable area, while Moeen struggled and made way for Root for 13 overs.
After 48.1 overs and 142 runs, Broad ended the partnership, seeing off Bravo for 69.
Broad came round the wicket and tightened his line just enough to see a thin edge nestle in Buttler’s gloves.
Brathwaite, joined now by chief agitator Marlon Samuels, was in it for the long haul and reached a fourth Test century in the penultimate over.
Should he prove equally hard to shift today, it seems a drawn Test and a winner-takes-all decider in Barbados beckons.
Brathwaite said: “I kept working hard and I’m very proud.
“I grew up watching England so I’m very happy to make a hundred.
“England were aggressive at the start and I thought they bowled really well.
“I learned my powers of concentration from my father – I used to bat really fast.
“We start afresh (today) and take it from there,” added Brathwaite.