Armed with a first-innings lead of 104, England slipped to 52-3 as Jonathan Trott and Alastair Cook failed again.
However, Gary Ballance and Joe Root saw the tourists to 116-3 – 220 ahead – at the close of day three in Antigua.
Earlier, James Tredwell took 4-47 to bowl West Indies out for 295 despite Jermaine Blackwood’s unbeaten 112.
Blackwood’s maiden Test century, in his sixth match, and two early wickets for the potent Jerome Taylor went to waste somewhat as West Indies failed to maintain the pressure in the evening session.
Ballance, initially cautious, and the typically energetic Root batted with increasing freedom against a tiring attack as they made 44 and 32 not out respectively.
While England can be satisfied with their lead, especially given West Indies must bat last on a pitch showing occasional signs of variable bounce, their top order remains a cause for concern.
Having slipped to 34-3 in the first innings, England again lost both openers cheaply.
Trott, promoted to the top of the order in his first Test since November 2013, followed up his three-ball duck on Monday by making four.
He was caught behind driving at Taylor, who found considerable swing with the new ball, and a leaden-footed Cook drove to gully to depart for 13.
First-innings centurion Ian Bell was even more culpable, run out for 11 after a half-hearted attempt to regain his ground following an aborted single to backward square-leg.
But Ballance, whose early caution made way for the odd punched drive, eased England’s nerves, sharing an unbroken stand of 64 with Root to help convert a position of some peril into one from which the tourists can press for victory.
Tredwell said: “That partnership at the end got us into a decent position, so we’ll look to build a sizeable lead and assess how long we need to bowl them out.”
England’s stuttering start with the bat took some of the gloss of an impressive bowling performance led by Tredwell, who claimed three of the six West Indies wickets to fall after they resumed on 155-4.
On the day that fellow off-spinner Moeen Ali’s addition to the squadfor the final two Tests was announced, Tredwell mixed his pace and flight adroitly on a surface offering minimal turn.
“By putting in a performance I’ll hopefully give [the selectors] a few headaches,” said Tredwell. “Who’s to say we both might not play in the next game?”
He landed arguably the biggest blow when he had Shivnarine Chanderpaul, advancing down the pitch, taken at the wider of two short covers for 46.
That ended a 41-over stand of 93 for the fifth wicket, and Denesh Ramdin – discomfited by Stuart Broad’s extra bounce – gloved down the leg side to strengthen England’s advantage.
However, Blackwood mixed unpredictable aggression with stout defence as he converted his overnight 30 into a superb 205-ball hundred.
Jason Holder helped add 49 for the seventh wicket before driving Tredwell tamely to Ballance, and lack of spin did for Kemar Roach as West Indies’ last three wickets fell for the addition of three runs.
James Anderson took the final wicket, leaving him one shy of Ian Botham’s England record of 383. He will be expected to surpass it on the fourth afternoon.