The West Indies still trailed the hosts by 35 runs but showed application to negotiate a lengthy final session for the loss of just one wicket.
Shivnarine Chanderpaul, almost inevitably, was left unbeaten after a painstaking 34 from 93 deliveries, while Marlon Samuels supported him ably to reach 26 not out.
It capped a day when the West Indies had fought hard and endeavoured to get back into the contest, taking the last seven England wickets in the first part of the day for 149 runs to restrict them to 398.
But having built a 155-run first-innings lead despite the West Indies' best efforts, and making inroads into the tourists' batting line-up, England remain heavy favourites to wrap up victory on day four.
England had laid a platform from which to push on after solid batting on day two, but the West Indies had the better of the morning session to peg the hosts back.
Skipper Andrew Strauss was able to add just one run to his overnight total of 121 before he was caught behind off a lifting ball from Roach. The edge was missed by the umpire, but successfully detected by hot spot when the West Indies appealed.
Jonny Bairstow began his Test career brightly enough, glancing away a couple of boundaries against the impressive Roach and Edwards. But having driven Roach through the covers for four on his previous ball, his innings came to an abrupt halt on 16 when he was given out leg-before as Roach went full.
Matt Prior was typically purposeful, adding 19 at quicker than a run a ball before he played across a straight full delivery and handed Shannon Gabriel his first Test wicket, while in the next over Darren Sammy accounted for Tim Bresnan with a ball that lifted higher than the Yorkshireman expected, leaving him to fend an edge to the wicketkeeper. Ian Bell, meanwhile, progressed stoically if quietly to 38 by lunch.
It looked as if the West Indies’s resurgence would continue unimpeded when Stuart Broad perished in the first over after the interval, but a cameo from Graeme Swann swung the momentum back to the home side.
He added 30 from just 24 balls with some crisp strokes before being clean-bowled by Gabriel, who then claimed a third scalp when Bell heaved to midwicket in search of runs and fell with 61 to his name.
Broad and Anderson soon settled into a familiar groove in pursuit of West Indian wickets, but with less swing on offer than they had found in the first innings, they had to be patient.
In the end it was Bresnan who made the breakthrough in his first over. His first four deliveries cost 10 runs, but his fifth drew a faint edge from Adrian Barath, sparking a mini-collapse from the tourists.
A desperate couple of overs followed, with Kieran Powell falling for the sucker punch of the short ball, lofting a pull off Broad straight to Bell, lurking at midwicket.
And in the final over before tea a mix-up between Darren Bravo and Kirk Edwards saw the latter dismissed after a clinical throw from Bairstow at cover-point.
The West Indies regrouped, with Chanderpaul emerging at the tea break with the West Indies limping at 36 for three.
Despite scoring at a snail’s pace as Anderson and Bresnan bowled parsimoniously, the pair drew the sting from the England attack.
Bravo eventually perished for 21, misjudging a ball from Swann and allowing it to rock back his off stump.
But Samuels picked up where he left off, frustrating the England attack.
The West Indies have shown determination throughout the three days, and still find themselves well behind the match, so England’s attack will have to rouse themselves for a final effort if they are to wrap up the contest on Sunday.