Impromptu victory processions broke out across the country, with some of the loudest celebrations taking place at Dhaka University where around 5,000 people had been watching the match in Adelaide on a big screen.
The crowds, including hundreds of girls, started dancing and chanting "Bangladesh, Bangladesh" as Rubel Hossain clean-bowled last man James Anderson to guide the Tigers to a 15-run victory their first ever place in the quarter-finals.
The Tigers have been international cricket's whipping boys for much of the last two decades and few experts expected them to get out of a group that included joint hosts New Zealand and Australia, as well as Sri Lanka.
Fellow student Tamir Islam, who is a keen cricketer, said: "I am sure no petrol bombs or molotov cocktails will go off today. We're united in cherishing the biggest triumph in our sports history."
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Social media was flooded with people celebrating and photos of a Bengal tiger chasing James Bond starring Daniel Craig.
"There's screaming and whooping from every yellow hat on a construction site," Australian Sarah-Jane Saltmarsh, who lives in Dhaka, wrote on her Facebook page.
Bangladesh Prime Minister Sheikh Hasina, a cricket buff herself, sent a message of congratulations to the team just moments after the victory in Australia while the sports minister announced bonuses for each player.
The country's opposition leader Khaleda Zia, who has been confined to her office in Dhaka for the last two months as part of a long-running chapter of political unrest, also congratulated the team.
Former national team captain Akram Khan, who skippered Bangladesh in the Tigers' first World Cup appearance in 1999, rated the victory over England as one of the team's finest moments.