The first strike killed 30 people in the Mansour district, where fans were marking Iraq's victory, which takes the side into the final of the Asian Cup.
Twenty died in the next blast, at an army checkpoint in east Baghdad.
Thousands had filled the streets of the capital, dancing and waving flags in a rare moment of national unity.
Police said the two attacks deliberately targeted the jubilant supporters.
The first explosion occurred about 1830 local time (1430GMT) in the western neighbourhood of Mansour, where a car exploded in a crowd of cheering fans.
"I was in a car with my friends, people all around were celebrating and then there was a huge explosion and a lot of fire," an anonymous eyewitness told the AFP news agency.
Death and joy
Less than an hour later a suspected suicide car bomber struck in the midst of dozens of cars filled with supporters near a military checkpoint in the eastern district of Ghadeer.
The BBC's Nicholas Witchell in Baghdad says the win was a genuine moment of national pride and pleasure, which crossed the sectarian divisions between Iraq's different communities.
Just as the Iraqi team has Sunni and Shia Muslims and Kurds playing alongside each other, the celebrations brought members of all those communities out onto the streets, he adds.
They cheered and waved Iraqi flags, sharing, perhaps, the first such moment of national pride in recent years, our correspondents says.
The team beat South Korea 4-3 on penalties in the semi-final match in the Malaysian capital, Kuala Lumpur. Iraq will now face Saudi Arabia in the final.
There were celebrations across Iraq. "I am nearly crying for joy," 30-year-old fan Nuri Najjar told Reuters in the southern city of Basra.
"Iraq's victory with this harmonious team represents the way we should all live together."
Separately, at least one person was reported to have died after being hit by stray bullets fired in celebration, an Arab tradition popular in a city awash with guns.
Güncelleme Tarihi: 26 Temmuz 2007, 12:42