Bairstow's unbeaten 108 off 48 balls, with eight fours and nine sixes, see Punjab secure the win with eight balls to spare
The 30-year-old part-time bowler, whose action was reported after Zimbabwe's defeat in the second Test against Bangladesh on Friday, had 21 days to undergo testing, the ICC said on Saturday.
Off-spinners Sachithra Senanayake (Sri Lanka), Kane Williamson (New Zealand), Prosper Utseya (Zimbabwe), Sohag Gazi (Bangladesh) and Saeed Ajmal (Pakistan) have all been reported for suspect bowling actions in recent months.
Three of them -- Senanayake, Williamson and Ajmal -- were subsequently banned from bowling.