Brathwaite was 55 not out and with him Marlon Samuels on nine not out as West Indies -- set a mammoth 456 to win or bat out five sessions for a draw -- fought hard on a weary Sheikh Zayed Stadium pitch.
They still need another 370 more runs with eight wickets in hand to clinch an unlikely win. Pakistan had declared their innings at 227-2 at lunch, with Asad Shafiq on 58 not out and Younis Khan 29 to give their bowlers enough time to force a 2-0 lead in the three-match series.
West Indies' task of saving the Test was made even more difficult after they lost Leon Johnson (nine) and Darren Bravo (13) with the total on 63. Johnson tried to sweep a delivery from leg-spinner Yasir Shah only to drag it on to his stumps after hitting the bat and glove.
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Shafiq scored his second fifty of the match with three boundaries after Azhar Ali was dismissed for 79.
Resuming at 114-1 Pakistan were unable to score quick runs as West Indian captain Jason Holder kept a tight field, with only five boundaries in the session.
Ali, who scored a career best 302 not out in Dubai, edged Miguel Cummins to slip where Holder took a sharp catch for the fast bowler's first wicket in the series. Ali hit five boundaries during his 137-ball stay at the crease.