India sealed a deal to bring Formula 1 to the world's second most populous nation, behind China, four years ago and the event is being funded by the private company Jaypee Group, rather than being supported by the government.
Force India team principal Vijay Mallya has championed an event in India since he first brought an F1 car over to the country in the 1980s.
Three decades on, this weekend's landmark event marks the fulfilment of a dream.
"It was like a dream come true," enthused Mallya. "If I was not glued to what was happening, I might have shed a tear or two out of pride and joy.
"I'm a relieved man. Racing is in my blood and putting an Indian team on the grid was a huge moment.
MARTIN BRUNDLE ANALYSIS
“I'll be sad to leave India. For me it's been very enjoyable and a great success for Indian motorsport and Formula 1. There is a lot of poverty downtown. We can't change that but a facility like this can be a springboard. Year two and year three will be interesting, though. How many of the cricket and Bollywood stars will be on the grid then?”
"Our following has come on leaps and bounds and this race will be a huge boost for Formula 1 in India."
Organisers were still working on the track when the teams arrived on Wednesday, but Mallya insisted the venue was ready with just a few finishing touches in order.
"The infrastructure and facilities are already there," he added. "The people in Paddock Club [hospitality] are extremely comfortable, we're comfortable in our motorhomes and the drivers love the track.
"One might complain a little about the finishing but that doesn't impede the experience. With time, they'll fix the little bits. It's all there and is something to be proud of."
Vettel, who sealed his 11th win of the season with victory in India, praised the organisers and track layout: "I'm proud to win the first Indian Grand Prix. It's a great honour to put our name on the race. All the drivers are thrilled with the track.
Plan worked perfectly - Schumacher
"What the people did here in the short amount of time to put up this arena is incredible. It's very different to what we know from Europe but very inspiring if you keep your eyes and ears open.
"Sure there are a few things they can improve on but that is normal. Now they know what to fix and they will do so for next year."
After finishing seventh in India, McLaren's Lewis Hamilton said: "The Indians did a fantastic job this weekend. The track was great and we've been treated like kings and I'm grateful for that."
Michael Schumacher, who finished fifth for Mercedes, said: "I have big compliments to make. If you imagine these guys do their jobs for the first time, I'm pretty sure things have been difficult but it worked out perfectly fine.
ANDREW BENSON'S BLOG
“India has its share of problems - that is well known. Equally, though, if you spend any time there, it is difficult not to fall under its complicated, captivating spell. After a debut that was unanimously hailed as a success, F1 is hoping that India will come to feel the same way about its new arrival”
"The circuit is a great challenge and has a fantastic nature, [providing a] good spectacle [with] overtaking and a good challenge for us, and organised very much in order."
Narain Karthikeyan, who was the only Indian on the grid when he stepped into the HRT for a one-off appearance, stressed how Formula 1 and the Indian Grand Prix is economically important to his country.
"There was a big crowd today so it was a big success for us," said Karthikeyan. "Motorsport is on a high in India.
"We are competing with our neighbours - China, Malaysia and Singapore - in the economy and on so many other things, so having a high-profile event like this gives you a boost.
"There is a lot of disparity but we're a country of a billion. We're very passionate people and very happy to have F1 here."
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