West Indies had reached 141 for 4 at tea as they added 103 runs in the post-lunch session after struggling at 38 for 3, having lost the key wickets of Darren Bravo (11) and Marlon Samuels for no score.
At the break, Brathwaite was on 55 and Roston Chase 43 not out, the pair adding 73 runs for the unbroken fifth wicket stand.
West Indies trail Pakistan's first innings total of 281 by 140 runs with six wickets intact. Pakistan managed just one wicket in the second session with Jermaine Blackwood caught at gully off fast bowler Mohammad Amir for 23.
Brathwaite took a single off spinner Mohammad Nawaz to complete his 12th Test fifty, having so far hit six boundaries in his 123-ball stay. Chase has also struck six boundaries in his confident 82-ball stay.
West Indies had lost the key wicket of Bravo before lunch. Bravo miscued a drive off a flighted ball from spinner Zulfiqar Babar and was smartly snapped up by a diving Mohammad Amir at extra cover, his first catch in 20 Tests.
West Indies got off to a disastrous start, with opener Leon Johnson trapped leg-before by paceman Wahab Riaz in the fourth over for just one.
Marlon Samuels also did not last long, trapped leg-before by leg-spinner Yasir Shah without scoring to leave West Indies struggling on 38-3.
Earlier, leg-spinner Devendra Bishoo finished with figures of 4-77 while fast bowlers Shannon Gabriel took 3-67 and Alzarri Joseph 2-57 to dismiss Pakistan for 281. Pakistan added 26 to their overnight score before losing Amir for 20 and Shah for 12, both to Joseph. The pair added 32 for the ninth wicket.
Pakistan are targeting a 3-0 whitewash after winning the first Test in Dubai by 56 runs and the second in Abu Dhabi by 133.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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