- Tag results for Joe Root
Jimmy Anderson overtook Australia's Glenn McGrath to become the most successful fast bowler in Test history, with 564 wickets.
Joe Root's England side are now just one point behind South Africa and Australia, who are both on 106 points with the former marginally ahead on decimal points.
The day certainly belonged to Cook, who scored his 33rd hundred his last appearance to join a select band of players having scored a hundred on debut and final Test.
Cook's 181-run third-wicket partnership with his successor as captain, Joe Root, who is unbeaten on 92, has taken England's lead to 283.
Buttler and Stuart Broad frustrated India with a ninth-wicket stand of 98 as, yet again this series, England bounced back with the bat after a top-order collapse.
Cook, who walked out to a guard of honour from the India team, was soon into his stride with two trademark boundaries off successive balls from fast bowler Jasprit Bumrah.
Root said that Cook had informed him of his retirement decision in Southampton, and that this wouldn't be a distraction ahead of or during the fifth Test.
Bairstow had broken a finger keeping during India's 203-run win in the third Test at Trent Bridge.
Root said he was confident of a win with so many bowling options at his disposal as England's potent attack dismissed world No 1 India for 273 and 184 in the two innings to secure the win.
Moeen Ali started the fourth test as England's second spinner. By the end of it, he was England's No. 1 bowler.
Buttler scored 69 and put on vital lower-order partnerships with Ben Stokes and Sam Curran as England recovered from 122 for five to finish at 260 for eight at stumps on day 4.
England now have an overall lead of 125 runs with Jos Buttler (22, 39 balls) and stodgy Ben Stokes (20, 79 balls) at the crease.
Starting from overnight 6-0, England made a slow start with openers Keaton Jennings and Alastair Cook putting on 24 for the first wicket.
Meanwhile, England have included Moeen Ali and Sam Curran in the starting XI.
Before the Nottingham Test, questions were raised about the composition of the India team. Now, the same people are saying there is no need to fiddle with the winning eleven! If Virat Kohli goes into