Bairstow, along with fit-again Jason Roy (66 off 57 balls), added 160 for the first wicket on a track where Kuldeep (1/72 in 10 overs) and Chahal (0/88 in 10 overs) had a forgettable day.
It took an impressive diving effort from substitute fielder Ravindra Jadeja in the deep to dismiss Roy off Kuldeep in the 23rd over but the platform was set by then.
Bairstow lost a bit of sting after Roy's dismissal and finally was out for 111 that had 10 fours and half a dozen sixes.
India (11 points from 7 games) will need to win at least one of their remaining two games -- against Bangladesh and Sri Lanka -- to seal the last four spot. India's defeat on Sunday will also make Pakistan's (9 points from 8 matches) chances of qualifying for the semifinals a tad difficult.