Sibley had frustrated the West Indies with a near eight-hour hundred during England's 113-run win in the second Test at Old Trafford that levelled this three-match series at 1-1.
Ben Stokes - continued from where he left - was in top gear on the final day from the outset.
At the end of the day's play England were 37/2 with Ben Stokes (16*) and captain Joe Root (8*) in the middle.
Ben Stokes fell prey to an audacious reverse-sweep of pacer Kemar Roach - who finally got his first wicket of the series after 521 balls.
Stokes struck 176 – his second-highest Test score – as he put a tired West Indies attack to the sword, facing more balls than he ever has before in a Test innings.
The three-Test series in England will mark the resumption of international cricket after it was suspended in March due to coronavirus pandemic.
Barbados-born Roach returned to training this week and the paceman made it clear he expects to be heading towards England soon.
Bracewell, who has played 125 first-class games, which include 27 Test matches for New Zealand, has pocketed 376 wickets.
West Indies require another 323 runs with only six wickets, if a physically indisposed Darren Bravo comes out to bat in the later stages.
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