The 107-run partnership between Jaiswal-Akash Deep was a turning point in India's second innings.
Speaking in a video released by the BCCI, skipper Gill reflected on his second-innings century, calling it the most satisfying of his career so far.
Sai Sudharsan made the opportunity count in his comeback game with a fifty while Rishabh Pant suffered another injury as India played the old-fashioned way to reach 264 for four at stumps on Day 1 of the fourth Test in Manchester on Wednesday.
Rahul was the only prominent batsman to miss out on a significant score in India's 358 all out on day two of the four-day tour game in Sydney.
Rahul replaced Australian skipper Aaron Finch and has gained a spot to be at number three.
The series, to commence on June 20, will be played at Headingley in Leeds, Edgbaston in Birmingham, Lord's and The Oval in London, and Old Trafford in Manchester.
Home lad KL Rahul's innings led the celebrations at the M Chinnaswamy Stadium with a cracking century.
'Yeah, really pleasing, really happy and proud of the way we have all played and how we have represented our country.'
There were moments in past tournaments where we weren't able to finish games or capitalise on crucial situations. But this time, we learned from those experiences,
Star Sports, the official broadcasters in India, tweeted a clip of Brook playing mind games with Krishna.
'But I think if you look at a rebuilding sort of phase, I think India can cope with it better than most other teams'
Teenager Eddie Jack's call-up comes at a time when England's pace stocks are depleted with less than 10 days to go for the opening Test.
Indian captain Shubman Gill and his teammates also revelled in the win and expressed their pride and joy on social media handles.
In the ongoing IPL, LSG suffered a 20-run defeat to RR in their opening game of this year's IPL. KL Rahul-led LSG is currently languishing in the tenth spot with no points and a net run rate of -1.000 after its loss in the previous game.
In his first high-profile captaincy assignment, K L Rahul is looking to lead from the front and use the nuggets of leadership knowledge he has collected while observing the likes of Mahendra Singh Dhoni, Virat Kohli and Rohit Sharma.
A round-up of Sunday's action in the Syed Mushtaq Ali Trophy group stage matches.
'I told Jassi bhai, If I take five wickets, who should I hug?'
Jaiswal (87) became the first Indian batter dismissed between (80 to 99) at Birmingham.
Rahul has scored only 22 runs in three games but the coach said that there is no chance of replacing him
After the 2-1 series win against West Indies, India opener KL Rahul and skipper Virat Kohli have significant progress in the latest ICC T20I player rankings.
KL Rahul got instant success as captain of Lucknow Super Giants in the IPL and he put it mainly down to trusting his instincts, something he didn't do enough in his initial days as a leader.
Rahul, who was dropped in the middle of England Test series held earlier this year, will be looking to make a comeback in the Indian Test set-up with the two-match Test series against Bangladesh, starting September 19.
Ganguly said had the top-order batter applied a bit better, the result would have ben different.
In the team's first session ahead of the third Test, Bumrah seemed to be good spirits, constantly chatting with fellow teammates and at times with the travelling Indian media.
Former England captain Michael Vaughan feels Zak Crawley's time-wasting tactics at the end of the third day in the ongoing third Test was "as good a piece" he has ever seen, but said India can't complain as the visitors employed the same approach on the second day at Lord's.
Mumbai off to flourishing start in SMAT, beat Railways by 7 wickets
Rahul along with wicketkeeper batter Dhruv Jurel flew early to Australia, and will appear for India A in the second four-day game at the MCG.
Walking out with intent and flair, the wicketkeeper-batter smashed a quickfire 51 off just 56 deliveries in the morning session, propelling England to a strong 387.
Former cricketers Nasser Hussain and Michael Atherton lampooned England's top order for their early collapse
Gautam Gambhir seemed in no mood to laud individual brilliance like the twin hundreds by Rishabh Pant
K L Rahul eases concerns surrounding his fitness ahead of the first Test against Australia, starting in Perth, by batting comfortably in the nets on Sunday.
Aus ODIs: Bumrah, Gill workload to be discussed, battle between Jaiswal and Abhishek
'His hands are quite sore. We want to get his confidence back up.'
England gained the upper hand after a rain-hit first day of the final Test against India at The Oval on Thursday
Shubman Gill scored a record-breaking 269 and their seamers struck early to put the tourists in a commanding position at Edgbaston on Thursday.
'There will be things that happen between the two teams but both teams know there's a line you can't cross but it's not really been troubled too much'
England Lions were 192 for 3 in 46 overs in reply to India A's 348 at stumps on the second day of their second unofficial Test, in Northampton on Saturday.
The Capitals sit pretty at the top with 10 points from six games, while the Titans trail close behind with eight from as many outings.
India Test captain Virat Kohli on Wednesday declared fit-again K L Rahul as the team's No.1 choice opener, ruling out veteran Gautam Gambhir's chances of playing in the second Test against England, starting in Visakhapatnam, from Thursday.
Mighty impressed with Shubman Gill's footwork in difficult English conditions, former India skipper Sourav Ganguly is expecting the young skipper to score truckloads of runs in away conditions