Brathwaite anchored the West Indian innings with a 206-ball 95 not out after they were struggling at 38-3, putting two solid stands of 83 each with Roston Chase (50) for the fifth wicket and with Shane Dowrich (47) for the sixth.
At close skipper Jason Holder was unbeaten on six as West Indies were 244-6, just 37 runs away from Pakistan's first innings total of 281.
This gives West Indies a good position for the first time in the series against Pakistan who are targeting a 3-0 clean sweep after winning the first Test by 56 runs in Dubai and the second by 133 runs in Abu Dhabi.
"There will be no butterflies," said the 23-year-old from Barbados.
"For me helping the West Indies to a good lead will be more important and I will do my best to achieve that."
West Indies lost Jermaine Blackwood for 23 soon after lunch and it looked like they would once again concede a lead but Brathwaite held the innings well with Chase and Dowrich.
Chase hit leg-spinner Yasir Shah for a straight six to bring up his fifty but was caught in the slip off Mohammad Amir in the next over. His 89-ball stay was spiced with six fours and a six.
Dowrich was finally bowled by Riaz from an inside edge.
West Indies were struggling when they lost the key wicket of Darren Bravo for 11 before lunch.
Bravo miscued a drive off a flighted ball from spinner Zulfiqar Babar and was smartly snapped up by a diving Amir at extra cover, his first catch in 20 Tests. Amir had no catch in his first 19 Tests -- most matches without a catch for a player from the start of his career.
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.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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