Their spirit and energy in that final passage of play was probably sparked by a 123-run seventh-wicket partnership between captain Shakib Al Hasan (63) and wicketkeeper-batsman Nurul Hasan (64) just a couple hours earlier which saved the tourists from the ignominy of an innings defeat.
They had come together just before lunch at 109 for six and proceeded to frustrate the West Indies through the entire afternoon session.
It took the new ball and the persistence of Roach to separate them after tea with the Barbadian taking three of the last four wickets for his 10th five-wicket innings haul in Test cricket.
His dismissal of Ebadot Hossain, uprooting the tailender's middle-stump, to end the innings was also his 50th Test wicket at the venue, the most by any bowler.
He also drew level with Michael Holding on 249 wickets for joint-sixth position on the list of all-time leading West Indies wicket-takers in Tests.
'Role model' Roach
Roach had bowled an opening spell without success however at the start of the day when Bangladesh resumed their innings at 50 for two and it took the clever variations of seam bowling all-rounder Kyle Mayers to effect the first strikes in having Najmul Hossain caught at first slip and struggling former captain Mominul Haque trapped leg-before.
"Trying to make the batsmen play at every delivery and utilising the conditions are really strong points for me and those tactics worked again today," said Mayers.
"Kemar is a role model for me and the rest of the guys. He gives 100 percent every time he goes onto the park and he is always looking to perform. I wish him all continued success and hope he goes on to get 300 Test wickets."
Roach added to those early successes by Mayers in dismissing Liton Das and opening batsman Mahmudul Hasan for a hard-fought 42 and it seemed the match would all be over by mid-afternoon with a comprehensive innings victory for the home side.
However Shakib, even though he remained prone to indiscretion, and Nurul displayed the sort of character and effort that has been missing from most of their team's efforts in this Test with the captain completing his 29th Test half-century and the wicketkeeper-batsman notching his second.
Frustrated by their lack of effectiveness with the older ball, Brathwaite wasted no time in taking the new ball as soon as it became due after 80 overs just after tea.
There was almost immediate reward when Shakib miscued a drive at Roach straight to the West Indies captain at short extra-cover.
That was effectively the end of the resistance as Nurul fell to Roach two overs later.
Alzarri Joseph scattered the stumps of Mustafizur Rahman but it was left to Roach to complete the job and he did so in style, and to much acclaim and appreciation from his delighted teammates.