Kumble's 110 not out was the centrepiece of India's 664, their highest Test innings total against England, at The Oval here Friday.
England, at stumps on the second day of the third and final Test, were 24 for one still needing a further 441 runs just to avoid the follow-on.
All 11 India batsmen made it into double figures but, in a line-up featuring the likes of Sachin Tendulkar, Rahul Dravid and VVS Laxman, it was Kumble - appearing in his 118th Test - who became the first India player this series to reach three figures.
"We had a team meeting a couple of days back and I just mentioned it's about time our batters scored a hundred in the series and I never thought I would have to do it," Kumble said.
The 36-year-old leg-spinner, who needs just three more wickets to move past Australia's Glenn McGrath into third place in the list of Test cricket's most successful bowlers, added: "I jokingly again mentioned that at tea-time when I was on 60 not out saying maybe it's my time to go out there and get a hundred.
"I always believed it was possible but I never thought I would have to wait 118 Test matches."
There were eight partnerships of fifty or more in the innings with wicket-keeper Mahendra Dhoni, who made a rapid 92 off just 81 balls, and Kumble putting on 91.
Such was India's dominance on a placid pitch, that Kumble and last man Shanthakumaran Sreesanth added 73 - a 10th wicket record for either side in an England-India Test.
Kumble, whose side went 1-0 up in the series with a seven-wicket win in Nottingham after holding out for a draw with one wicket standing during the first Test at Lord's, was 24 runs short of his century when Sreesanth came out to bat.
"Sree kept saying 'you deserve a hundred and I'll hang around'," Kumble explained.
Kumble, with Tendulkar having made 82 earlier in the innings, reached his hundred when a bottom edged cut off part-time spinner Kevin Pietersen went through the legs of England wicket-keeper Matt Prior.
"You always get four runs when you score there," joked Kumble, whose wait of 118 Test matches for his first hundred at this level was a record.
"I have achieved what everyone dreams of when you start playing. Throughout my career I've put a price on my wicket. I know as a bowler how difficult it is to get a wicket."
The elated reaction of India's players in the dressing room said much about their respect for Kumble.
"You can make out from his expression when he got his hundred, you don't see Anil celebrating like that most of the time," said wicket-keeper Dhoni.
"It was amazing, a remarkable moment. I am happy I got 92. It was needed from the team's point of view."
Three England bowlers conceded more than 100 runs each and left-arm quick Ryan Sidebottom had 93 against his name before a side injury meant he stopped bowling at lunch.
England were left on the brink of losing their six-year unbeaten record in home Test series.
But coach Peter Moores said they had to remain upbeat: "You never really say you just want to save the game because that's a negative way of looking at it."
And Kumble added: "I think it's still a good wicket. I got a hundred, that should give out a message."