The 22-year-old seamer's mother, Sharon, died before play on the third day following an illness and Joseph declined the offer of time away from the match to take the field with his team-mates.
He batted briefly as the Windies established a 119-run first-innings lead in the morning and then dismissed Joe Root and Joe Denly as England stuttered to 75 for four at tea - still 44 adrift.
Joseph, playing his first Test on his home island of Antigua, also had Ben Stokes dropped on a duck, performing with great courage and skill despite his loss.
England, joining their opponents in wearing black armbands as a sign of respect, began by turning in another solid bowling performance in the morning, taking the Windies' last four wickets for 34.
Jason Holder and Kemar Roach both succumbed to James Anderson's probing outside off stump, bringing Joseph to the crease to a generous round of applause. He made seven before poking Stokes low to Rory Burns, with his major impact still to come.
Darren Bravo was last man out, continuing a painstaking innings which began on the second afternoon and saw him reach 50 in 215 deliveries. That his five-and-a-half hour marathon closed with him walking down the wicket to Moeen Ali and being stumped was an unbecoming end.
England's opening pair somehow negotiated a fierce opening blast with the new ball - including at least one terrifying bouncer from Roach to Burns and Denly being dropped at fine-leg after pulling Shannon Gabriel.
Burns let his guard down when Holder entered the fray, leaning back and inexplicably guiding his first delivery straight to third slip.
Jonny Bairstow also fell to the home captain, mis-timing a couple of balls and responding by aiming a mighty drive at the next full delivery. With an angled bat and a healthy gap, he promptly lost his off stump.
The spotlight then fell to Joseph, who got one to nip back into Root before scurrying through to the wicketkeeper. The bowler appeared largely disinterested but the entire cordon felt differently and DRS showed a hint of glove before a heavier touch off the thigh pad.
There was no doubt about his second wicket, Denly dramatically misjudging a leave and seeing the ball scatter his stumps.
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