Bairstow's unbeaten 108 off 48 balls, with eight fours and nine sixes, see Punjab secure the win with eight balls to spare
Captain Misbah-ul-Haq made 96 and Sarfraz Ahmed 56 to lift the hosts to an imposing first-innings total as they bid for a victory that would give them an unassailable 2-0 lead in the series. Younus Khan struck a century on the first day.
West Indies lost both openers lbw, Leon Johnson falling to fast bowler Rahat Ali for 12 and Darren Bravo to spinner Yasir Shah for 43.
Kraigg Brathwaite and Marlon Samuels shared a steady third-wicket partnership of 41 but both fell in quick succession shortly before the close to give Pakistan the upper hand.
Samuels was caught by Sami Aslam at slip off Rahat for 30 and two balls later Brathwaite was needlessly run out for 21 following a mix-up with his partner Devendra Bishoo.