Complete Coverage of India vs England Series on Cricket.com.pk
The South Africa-born left-hander topscored with 112 as the visitors, trailing 2-0 in the five-match series, ended the day on 288-5 at the Wankhede Stadium.
Jennings was dropped before he had scored and took until his 12th ball to get off the mark but once he opened his account he batted fluently.
“I woke up at 5:00 am thinking I’d missed the bus so I jumped out of bed and panicked about where everything was,” said the 24-year-old opener.
“But then I settled myself down when I saw the time. If someone had told me this morning that you’ve got a Test match hundred I would have bitten their arm off.”
Referring to his early close shave, Jennings said: “When the ball looped up to gully my heart was in my mouth and I thought ‘no you got a nought in your first innings’, but thankfully it went to ground and I went from there.”
Jennings, who was only called up to the squad after Haseeb Hameed was injured in the third Test, hit 13 fours, including a trio of audacious reverse sweeps during his 219-ball stay at the crease.
It was one of those sweeps that brought up his ton midway through the afternoon session, with Jennings raising his arms in delight.
“The emotion that went over me at that moment in time, the elation, the pride, the satisfaction to go to a Test hundred was really incredible, really special,” he said, describing it as a “dream come true”.
Jennings put on 99 for the first wicket with Alastair Cook as England made a strong start before the skipper was stumped on 46 by wicketkeeper Parthiv Patel after swinging at a Ravindra Jadeja delivery.
Joe Root could only make 21 before he was caught in the slips by Indian captain Virat Kohli off a spinning Ravichandran Ashwin ball but Moeen Ali helped guide Jennings to his ton, scoring a half-century of his own until he holed out.
– Ashwin strikes –
Jennings was dismissed shortly afterwards as Cheteshwar Pujara took a catch to give Ashwin his third wicket of the day, England slipping to 230-4.
Ashwin, ranked as the best bowler in the world, grabbed his fourth wicket when Jonny Bairstow was caught for 14 as India hit back.
Ben Stokes and Jos Buttler were unbeaten on 25 and 18 at the close.
Jennings, who was born in Johannesburg and captained the Proteas at under-19 level, became the latest South African-born English cricketer to score a ton on his international Test debut.
Andrew Strauss and Matt Prior both made centuries in their first outings while Jonathan Trott reached three figures in the second innings of his Test debut.
Jennings, whose mother is English, moved to England in 2011 after leaving school, committing himself to four years there so he could become eligible to play for the national side.
He opted for England to further his career in a similar move to Kevin Pietersen in the early 2000s.
Players who born abroad are eligible to play for England after spending four years in English county cricket, a policy that has attracted some controversy.