Chahal and Kuldeep were hit for 12 fours and as many as nine sixes as they hardly got any purchase from the Edgbaston track. Incidentally, Sunday's pitch was not the one which was used during Pakistan's game against New Zealand where Kane Williamson's part-time off-breaks turned right angles.
Mohammed Shami (5 for 69) got his maiden five-wicket haul but even he lost his bearings in the last two overs.
Jasprit Bumrah (1/44 in 10 overs) remained the only Indian bowler to finish with a sub-5 economy rate and the only maiden of the innings.
Bairstow (111 off 109 balls), 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.
Ben Stokes (79 off 54 balls) then used the platform to give the total an imposing look in a do-or-die game for the hosts.
From the start, they used big strides to reach to the pitch of the deliveries and smothered the spin for the big hits. If Bairstow targeted the arc between long-on to deep mid-wicket, Roy hit the straighter sixes.
In the second Powerplay with the field spread, one shot that England batsmen used to good effect was the reverse sweep as they exploited the short boundary on one side.
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.
Joe Root (44 off 56 balls) dropped anchor during a 70-run stand before getting out as Stoke hit six fours and three sixes to boost the total.