The victims were among the thousands of revelers who took to the streets of the capital after the country's national soccer team beat South Korea to reach the tournament's final against Saudi Arabia on Sunday in Jakarta, Indonesia.
The first attack took place about 6:30 p.m. when a bomber exploded in a crowd of people cheering near a well-known ice cream parlor in Baghdad's western neighborhood of Mansour, according to police and hospital officials. At least 30 people were killed and 75 were wounded, an Interior Ministry official said.
Another suicide car bomber detonated his payload about 45 minutes later in the midst of dozens of vehicles filled with revelers near an Iraqi army checkpoint in the eastern district of Ghadeer, killing at least 20 people, including two soldiers, and wounding 61, according to the ministry official.
All the officials spoke on condition of anonymity because they were not authorized to release information.
The second attack occurred as Iraqis of all ages were packed on top of cars, pickups and minibuses, waving Iraqi flags and shirts, while others danced in the streets near the checkpoint. Men put towels over their heads or sprayed cars with water for relief in the hot summer weather.
Thousands of fans also gathered in the central district of Karradah to celebrate, dancing, beating drums and chanting "Iraq, Iraq." Elsewhere in city, traffic snarled as cars, Iraqi flags flying from their windows, moved slowly amid hundreds of fans. Motorists honked their horns.
The successful run in the Asian Cup has been a cause of much joy in this war-torn country, with Iraqis saying the mixed makeup of the team showed the country's rival ethnic and religious factions can unite despite years of sectarian violence.
Preliminary police reports said one person was also killed and 17 wounded by celebratory gunfire.
More than an hour after Iraqi goalkeeper Noor Sabri made the crucial save to win the match, gunfire could still be heard in many parts of the capital.
State television broadcast a warning from the Iraqi military urging residents not to engage in celebratory gunfire. But the warning appeared to have been ignored.
Five people were killed in the celebratory gunfire that followed Iraq's win over Vietnam in a quarterfinal match played in Bangkok, Thailand, on Sunday. But no other violence was reported in those celebrations.
Iraq and South Korea played to a scoreless draw through 90 minutes of regulation time and 30 minutes of extra time in the Malaysian capital of Kuala Lumpur. But Iraq won a penalty shootout 4-3 to advance to Sunday's final in Jakarta.
In other developments: