FIFA secretary general Jerome Valcke said the decision followed signs of progress on construction, financial guarantees and commitments by local organisers.
Officials said the stadium should now be ready by May 15, less than a month before the tournament starts.
"There was no other decision we could take but to keep Curitiba in," Valcke told a news conference in southern Brazil. "They understood the pressure we put on them."
Even as Valcke expressed renewed confidence, the severity of his ultimatum made clear that patience is running out at FIFA, which has warned for months that work was critically behind schedule at several stadiums across Brazil.
Curitiba is the most extreme case of the myriad delays plaguing host cities. Four other stadiums, including the venue for the prestigious opening match in Sao Paulo, also missed a December deadline for completion and are racing to finish work.
If FIFA had made good on its threat to exclude Curitiba from the tournament, it would have been a major embarrassment for Brazil and President Dilma Rousseff, who has promised "the World Cup of all World Cups" and touted benefits for a dozen cities chosen to host games.
A smoothly run tournament could help boost her popularity before she seeks reelection in October.
The run-up to the World Cup, however, has been an increasingly frantic effort to finish stadiums, renovate airports and prepare cities for hundreds of thousands of foreign fans.
Work at several airports is even more delayed than the stadiums and at least one terminal, in the city of Fortaleza, will be substituted with a temporary canvas structure. Five cities hosting matches will not complete the public transportation projects they had promised.
Complicating matters, Brazil has been besieged by periodic street protests since last June, with many demonstrators railing against the World Cup as a waste of money that would be better spent on education, healthcare and public transport.
Under pressure to ensure that mass protests do not disrupt the World Cup, Brazilian officials are spying on protest groups and debating stricter legislation aimed at containing street demonstrations.
Four matches are scheduled to take place at the stadium in Curitiba: Iran v Nigeria on June 16, Honduras v Ecuador on June 20, Australia v Spain on June 23 and Algeria v Russia on June 26. The stadium will not be used after the opening group stage.
- Sports & Recreation
- Jerome Valcke