Television networks showed people, many of whom skipped work for the day to watch the series on giant screens, dancing to drumbeats and flashing V for victory signs with their fingers.
An election rally by Deputy Prime Minister Lal Krishna Advani ahead of the April-May national polls had set up two giant screens for the cricket match to ensure crowds came to the venue rather than stay at home.
"Our team of eleven cricket players won the match as well as the hearts. The entire nation congratulates the team and pleased with their performance," Indian Prime Minister Atal Behari Vajpayee told the team in a message.
Cricket fans said they would celebrate all night and rated the victory as the most important after the 1983 World Cup win over West Indies in London.
"We are very happy that India has won, but a little sad that our captain Sourav Ganguly suffered a back injury during the match," said Rahul Dev, a cricket fan in New Delhi.
"We are hoping he recovers quickly and leads us to victory in the Test match series as well," he added.
Ganguly's family said they remained put before the television set to watch the entire match.
"It is a tremendous victory. All our family was glued to the television set to watch the grand end of the historic match," said Snehashis Ganguly, his elder brother in the Eastern Indian city of Calcutta.
In the riot-scarred western Indian Gujarat state's Ahmedabad city, clashes broke out between a group of Hindus and Muslims and the police had to fire teargas shells to bring the situation under control.
But nobody was seriously injured in the violence, police said.
India clinched the series 3-2 to record their first title win in Pakistan after five failed attempts between 1978 and 1997.
The Indians will attempt to rectify their record of never winning a Test match in Pakistan when the three-Test series starts in Multan on Sunday.