People of all ages made up a victory procession in the Dhaka University campus immediately after the four-wicket verdict, Bangladesh's first win against the former world champions.
Young men beat drums, waved national flags and honked motorcycle horns as they gathered to celebrate the victory.
"We have shown once again that we can beat any team. Our players have proved that they deserve a place in top-class cricket," said Hamidul Haq, a Dhaka University student.
The biggest celebrations took place in the northern town of Bogra where the Bangladeshi cricketers pulled off the memorable victory in front of 30,000 spectators at the Shaheed Chandu stadium on Wednesday.
The revellers sprinkled coloured water and flower petals, beat drums and shouted slogans such as "Long live Bangladesh".
The country's legislators - both from the government and opposition - hailed the victory and unanimously adopted a thanks-giving resolution at the national parliament to congratulate the Bangladesh cricket team.
"This historic victory of the Bangladesh tigers will enhance the image of the country, especially in the arena of world sports," the parliament observed in the thanks-giving motion, the state-run BSS news agency said.
In June last year, fans held similar celebrations after their team beat world champions Australia in a One-dayer in Cardiff.
Bangladesh have also beaten India and Pakistan in their 10 wins in 116 previous One-dayers. Their other victories have come against Zimbabwe, Kenya, Scotland and Hong Kong.