Joe Denly (20) fell in the next over, pinned by Shannon Gabriel, and England were in strife when Root wafted at a wide ball from Joseph and nicked behind.
Earlier, England declared on 361-5 after Joe Root was out for 122.
He added: "The battle was a good contest".
Gabriel was given an on-field warning by the umpires about using abusive language. "I think they can sometimes be caught in the moment and not always say what you want to say or think you're saying", the 28-year-old said.
Darren Bravo perished shortly after the resumption to another Root slip catch and the delighted fast bowler returned after some resistance from Shane Dowrich (38) to polish off the innings and complete the five-wicket haul when he yorked last man Shannon Gabriel.
Acting US Defense Secretary makes unannounced visit to Afghanistan
So far, though, he noted that the Taliban have been unwilling to take this step, arguing that the government is illegitimate. Acting secretary of defense Patrick Shanahan greets an Afghan commando at Camp Commando, afghanistan, on February 11, 2019.
At the end of day three, England were 325-4 in the second innings, with a commanding lead of 448 runs with Root and Ben Stokes at the crease.
It is also meant to cover language of a personal, insulting, obscene and/or offensive nature relating to a family member of the Player, Player Support Personnel, Umpire or Match Referee at whom it is directed'.
West Indies coach, Richard Pybus, said they would look into the incident.
There were positives for England - off-spinner Moeen bowled tidily and captain Root found form with the bat - but ultimately, it came too late for the series.
Roston Chase struck his fifth Test hundred but West Indies crashed to a heavy 232-run defeat to England, on the penultimate day of the third and final Test here Tuesday.
'The more players, fans, clubs and organisations that stand up for equality in sport, the sooner we kick discrimination out and make sport everyone's game.