Having whitewashed New Zealand at the beginning of last week, England went straight into an encounter with India, the final game of last year's series having been postponed due to coronavirus.
With India having posted 416 in their first innings and ultimately setting England a target of 378, the tourists were clear favourites to wrap up a 3-1 series win.
However, Bairstow and Joe Root put on one of English cricket's greatest partnerships in recent memory to get their team over the line in style.
The pair compiled an unbeaten fourth-wicket partnership of 269 runs, Root taking centre stage with 142 runs from just 173 deliveries to solidify the feeling that he is currently the world's best batsman in Test cricket.
Nevertheless, Bairstow's 114 represents his fourth century in five innings, a remarkable turnaround for a player who was fighting for his place in the team at the start of June.
England's run chase was also their highest in history, while it also ranks in ninth place in the all-time list of Test run chases.
After picking up the Man Of The Match accolade for hitting tons in both innings, Bairstow acknowledged the magnitude of what England have achieved since beginning their second innings on Monday.
Speaking to BBC Test Match Special, Bairstow said: "It is great. Every time I get to speak to you it is normally a good thing so long may it continue. Rooty obviously got this reward, it's extremely special how he's playing and for so long. It is awesome, it is a great environment at the moment. It is fantastic the way we're playing and everyone is really enjoying the success and that is a huge part of it.
"If Joe and I are out there doing it together we're in a really good place. We've been doing it for a long time together now. It is really special to knock off 378 with just three down. It is something that we'll never forget.
"After day two I got asked what do you think is too many and I said 'whatever they set we'll go for' and that's exactly what we did. The opening partnership deserves a huge amount of credit, for the way they went about it and the brand of cricket that we're trying to play, it was epitomised by that opening stand.
"It isn't going to work every time but the pressure and intensity which they put on world-class bowling takes a huge amount of guts, courage and skill."
England are not back in Test action until the middle of August, where they begin the three-match series against South Africa.
They will now embark on a month of limited-overs cricket, the T20 series against India getting underway on Thursday. body check tags ::