Paulo Bento’s side were unable to secure the heavy victory they needed to stand any chance of progressing to the knockout stages from Group G.
United winger Nani was one of his country’s most dangerous players and twice went close to scoring early in the second half with stinging drives that were blocked.
At that time, Portugal were leading 1-0 at the Estadio Nacional, courtesy of a comical own goal from John Boye, but Asamoah Gyan equalised for Ghana with a deft header just before the hour mark.
Cristiano Ronaldo, who earlier hit the bar with an audacious chip, scored the winner with 10 minutes to go but, despite the best efforts of the ex-Red and Nani, no more goals were forthcoming.
USA lost to group winners Germany 1-0 in the other game but qualified on goal difference, leaving Portugal to rue their 4-0 defeat to the Germans in their opening encounter.
It means United have five representatives in the last 16 in Brazil: Marouane Fellaini and Adnan Januzaj (Belgium), Patrice Evra (France), Robin van Persie (Netherlands) and Javier Hernandez (Mexico).
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