Cook famously keeps his cool when the heat is on anywhere in the cricketing world and there were no signs of any uncharacteristic perspiration at Eden Gardens either, even as he broke a 73-year-old record for the most hundreds by an Englishman.
Wally Hammond reached 22 10 days before the outbreak of the Second World War, and four others - including Cook and team-mate Kevin Pietersen - have equalled his mark.
But on day two of the third Test against India, "unflappable" Cook duly went one better - a few minutes after becoming the youngest batsman from any country to reach 7,000 Test runs.
Compton, in his first series at the age of 29, is two years Cook's senior and had a landmark of his own to celebrate during their stand of 165 when he made his maiden 50 at the highest level.
By stumps, Cook (136no) carried England to 216 for one - exactly 100 runs behind, with massive power to add - and into prime position to push for a 2-1 lead with one more match to play. Compton is struck especially by the calmness Cook transmits down the 22 yards, and felt privileged to be directly involved at such relatively close quarters.
"Standing out there today, looking up at the board and seeing those stats - 7,000 runs, the youngest player to do that, it was quite an amazing moment," he said. "I thought 'I'm batting with this guy; he's just got another hundred and he's the all-time leading English hundred-maker ...'."
Compton, grandson of the great Denis - who followed Hammond into bat at the Oval all those years ago - has trodden a very different path to international cricket.
He can only admire the prodigious Cook, a Test player at 21 and now with five successive centuries in his role as captain - another all-comers' record, of course.
"It speaks volumes that he's been able to do that from a young age, and still is a young player," added Compton. "A lot of players only find their feet at perhaps my age, 28 or 29, but he did it a long time before."