Kraigg Brathwaite and Jermaine Blackwood both hit centuries to keep England's bowlers largely at bay as the West Indies held solid for much of day three.
Brathwaite and Shamarh Brooks headed out in the first session with the Windies on 71-1, but the latter fell on 39 inside the opening 30 minutes of the day when he sliced Jack Leach's delivery to Chris Woakes.
Ben Stokes struck shortly after coming into England's attack midway through the session, dismissing Nkrumah Bonner for nine lbw, as the tourists look set to enjoy another fine day after declaring on 509-7 on Thursday.
Stokes should have had Blackwood lbw, only for the umpire to decline their appeals, with Joe Root choosing not to review.
That was swiftly proved a mistake, with the replay showing the ball would have hit halfway up leg stump, Blackwood then surviving an lbw review for what could have been Saqib Mahmood's first Test wicket.
Braithwaite and Blackwood made the most of their fortune, frustrating England throughout the second session to reach tea at 196-3, on 79 and 50 respectively.
Windies skipper Brathwaite nudged Leach for two to bring up his century from 278 balls, and his control remained as he allowed Blackwood to stake centre stage.
Blackwood picked off some sloppy Stokes deliveries, though he very nearly edged Leach to Dan Lawrence before he clipped England's spinner for a single to bring up his third Test ton.
His stand finally came to an end on 102, when Lawrence trapped him lbw but, despite a late review against Alzarri Joseph, West Indies held on to reach stumps on 288-4.
Brilliant Braithwaite leads by example
Braithwaite was quite simply sensational, with his 109 not out coming from 337 deliveries so far, and he will be there again at the start of day four.
He now has 10 Test centuries, with three of those having come against England.
A long day for England's bowlers
News of Mark Wood's tour-ending injury came at the start of the day and it was a difficult time for England's bowlers.
Leach has already bowled 44 overs, but has just one wicket to show for it, while Stokes has an economical 1-34 to show for his efforts, though it took a cameo from Lawrence (1-8) to make the late breakthrough.
France 37-23 Argentina: Les Bleus wrap up campaign with third win
France posted a comfortable 37-23 win over Argentina on Friday to make it three wins out of three tests at the Stade de France to conclude their Autumn Nations Series.
Having also beaten New Zealand and Japan in Paris this month, Fabien Galthie's side claimed four tries, including a superb solo effort from Louis Bielle-Biarrey, as they eased to victory against the Pumas.
The hosts led 30-9 at the break after Argentina's Julian Montoya and Juan Martin Gonzalez were both shown yellow cards in the first half, with Thomas Ramos slotting his third penalty of the game.
Tomas Albornoz made it 30-16 for Felipe Contepomi's visitors, but their hopes of a comeback were dashed as Bielle-Biarrey scored his fourth try in three games before Ramos made it 37-16.
Albornoz then cut the deficit to 37-23 with a two-pointer with nine minutes to play, but that wasn't enough to stop his side from falling to a defeat.
"We knew it was going to be an 80-minute game. We saw last week how Argentina went all the way against a good Irish team," France lock Emmanuel Meafou told TNT Sports.
"We are happy with the win. We have three from three [in the autumn] and we will look to build on that in the Six Nations next year."
Plymouth Argyle 2-2 Watford: Two-goal Gray rescues point for Rooney's side
Andre Gray scored twice against his former club to salvage a point for struggling Plymouth Argyle as they drew 2-2 with Watford on Friday.
Gray curled in an equaliser in the sixth minute of second-half stoppage time to seal a crucial point for Wayne Rooney's side in their bid for survival in the Championship.
The visitors made a quick start at Home Park when Ivorian striker Vakoun Bayo bundled in a cross from Yasser Larouci only eight minutes in.
Plymouth did, however, equalise against the run of play in the 23rd minute when Lewis Gibson's long ball into the box was met with a spectacular volley from Gray.
Watford regained the lead before the break when Imran Louza's free-kick was knocked back by Mattie Pollock, with centre-back Ryan Porteous on hand to steer the ball home.
But just as it looked like Watford would go home with all three points, Gray picked up the ball on the edge of the area and fired home a stunning effort beyond Daniel Bachmann.
Tom Cleverley's Watford sit in fifth place and trail leaders Sunderland by five points, while Plymouth are 17th with 17 points from 16 matches.
Bayern Munich 3-0 Augsburg: Hat-trick hero Kane smashes Bundesliga record
Harry Kane scored a hat-trick to become the quickest player to score 50 Bundesliga goals as Bayern Munich comfortably dispatched Augsburg 3-0 on Friday.
Kane opened the scoring in the 63rd with a penalty before netting a quickfire double in second-half stoppage time to smash the record previously held by Erling Haaland.
Despite controlling the early possession, Bayern were unable to make their dominance count, with Nediljko Labrovic rarely troubled in the opening 45 minutes.
The hosts maintained their dominance after the interval, with Leon Goretzka's looped header grazing the crossbar before Jamal Musiala went close soon after.
However, Bayern were awarded a penalty after a lengthy VAR review saw Mads Pedersen penalised for handling the ball, with Kane stepping up to score from 12 yards.
The England captain grabbed his second of the game in the third-minute of stoppage time following another VAR review which saw Keven Schlotterbeck sent off after tripping Kane inside the box.
Kane sent Labrovic the wrong way but was not to be denied a fourth treble of the season, brilliantly taking down Goretzka's searching ball before heading the ball home.
Data Debrief: HurriKane
Kane has now scored 50 Bundesliga goals in 43 matches. Before him, Haaland was the quickest player to reach 50 Bundesliga goals, having done so in 50 appearances in the competition for Borussia Dortmund.
He is also the quickest to reach that total for Bayern by some distance. Kane has reached that tally quicker than the likes of Gerd Muller (83 games), Mario Gomez (71 games), Roy Makaay (67 games) and Robert Lewandowski (64 games).
10 of Kane’s goals have come from penalties, while 32 of them have been with his right foot, nine with his left and nine with his head.
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