Eder saw a header pushed out by France goalkeeper Hugo Lloris, while Raphael Guerreiro hit the bar from a free-kick.
With 11 minutes of the extra period to play, the killer goal arrived as Eder held off Laurent Koscielny and drove a crisp shot into the bottom-left corner from 25 yards.
"Cristiano told me I would be scoring the winning goal," Eder said. "He gave me strength and positive energy.