Centre back Boye sliced a left-wing cross from Miguel Veloso into his own net after 31 minutes.
Portugal, who need to win big and hope Germany and the United States do not draw in Recife, had earlier gone closest to a goal when captain and world player of the year Cristiano Ronaldo hit the crossbar before being denied by a superb Fatawu Dauda save.
(Reporting by Justin Palmer, editing by Ed Osmond)
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