Captain Alves' spectacular ball-dribbling skills earned Brazil a first-half penalty that Gabriel da Silva converted after 22 minutes, while Goncalves' shot was deflected into the goal by goalkeeper Martin Baron in the second half to secure victory.
The win means Brazil are still unbeaten at 5-a-side Football in the Paralympic Games since it was introduced at Athens 2004, and they won the London 2012 title without conceding a goal.
They had goalkeeper Fabio de Vasconcelos to thank as he saved two penalties during the final and then went on to collect his gold medal. In previous Paralympic Games goalkeepers were not eligible for one.
For France, it is a first medal at Paralympic 5-a-side Football, but they rued three missed penalties from the eight-metre spot.
Spain, meanwhile, avenged their bronze-medal match defeat to Argentina at Beijing 2008 with a 1-0 penalty shoot-out win to clinch third spot.
When the clash ended goalless after normal time, Spain's Antonio Martin Gaitan scored the only penalty out of the six taken as goalkeeper Alvaro Gonzalez Alcaraz saved Angel Deldo's final spot kick to help seal the bronze medal.
Gaitan said: 'The goalkeeper stopped all their goals and we worked together. If we hadn't been a team we wouldn't have done it.
'Our target was to reach the final against France, but we lost that opportunity. We kept our heads up and we had a good mentality, so we're pleased with what we've done.'