Yorkshireman Bairstow, whose unbeaten 41 from 21 balls on debut against India last month in Cardiff cemented his place on this tour, hit eight sixes and four fours as England amassed 367-4.
Fellow youngsters Scott Borthwick and Stuart Meaker then took eight wickets between them as the hosts crumbled from 69-0 to 114 all out.
While there appears to be nothing wrong with Bairstow’s ball striking, he might need to brush up on his maths after the 22-year-old admitted he had no idea he’d passed the three-figure mark until he’d returned to the pavilion.
“This ground only had a little scoreboard which didn’t have individual scores, so I didn’t know about it until I walked back into the dressing room,” he said after launching the last ball of the innings deep over long on for six.
“I didn’t have a clue, even when I was walking off. But I got told in the dressing-room, and I was delighted to get that milestone.
“I had no idea at all. I was just ‘in the zone’ – batting every ball as it comes. When I got in and found out, I was over the moon.”
England play the first match of their five-game series against India in Hyderabad on Friday.