Gautam Gambhir's ploy to outbat the opposition was followed to the 'T' by his batsmen after Pujara scored his 32nd first-class ton only to set up the platform for Jackson, who was swiftly into the action plundering 105 off 114 balls with seven fours and five sixes.
India discard Karn Sharma also joined the free-hitting party with a quickfire 56 as Shreyas Gopal despite a second 'five-for' will not be happy with figures of 5/173.
India Blue bettered their first day's performance as they added 371 runs on the second day to the 336 on the first day.
The first session and a half belonged to Pujara who hit 24 boundaries in his 280 ball as he hit another 11 boundaries on the day adding to the 13 he hit on the first day.
He was a bit more cautious till he reached the landmark but opened up after that before chopping one onto his stumps off Gopal.
"I am disappointed that I did not continue. There were some problems sighting the seam of the pink ball and spotting the googly under lights," Pujara said after his knock.
The next session and half belonged to Jackson, who entertained the crowd with some clean hitting off the spinners over long-on and long-off while he pulled Dinda imperiously over deep square leg. he added 108 runs in just over 18 overs with Karn to pile on the misery of the already tired Green bowlers.
Jackson was into his 90's when he hit Jalaj Saxena over long-on for a six and then drove Gopal for a boundary to complete his 10th first-class ton.
He was the last man to be dismissed trying to clear Gopal, giving him his fifth wicket.
"I consider myself lucky. I was dropped in the 70s, the wicket was good and the ball was coming on nicely. When the new ball comes, it gets difficult (to sight) because the speed changes, the ball skids on at good pace, so making the minor adjustment takes a little bit of time," Jackson said after the game.
"Every match I score is important, but to score in such matches is very important because it is live and people are watching. It (the surface) should behave a little differently on days 3 and 4. Both the sides (of the ball) are scuffed up a little bit," he added.
Brief Scores: India Blue 707 in 176.3 overs (Cheteshwar Pujara 166, Mayank Agarwal 161, Sheldon Jackson 105, Gautam Gambhir 90, Karn Sharma 56, Shreyas Gopal 5/173) vs India Green. match to continue.