Bairstow's unbeaten 108 off 48 balls, with eight fours and nine sixes, see Punjab secure the win with eight balls to spare
Having elected to field after winning the toss, West Indies made full use of overcast conditions as Oshane Thomas took four wickets for 27 runs, while captain Jason Holder (3-42) and the returning Andre Russell (2-4) completed the demolition job.
The in-form Fakhar Zaman and Babar Azam got off to solid starts but were both dismissed for 22, sparking a middle order collapse that the former champions did not recover from.
Pakistan were bowled out in 21.4 overs for their lowest World Cup total since a paltry 74 against England at Adelaide in 1992, the year Imran Khan's team went on to lift their only 50-overs crown.