A sparse crowd in the Belo Horizonte stadium saw the Central Americans launch a late comeback but it was not enough to cut the deficit after Nigeria went 3-0 went up in 56 minutes.
Sadiq Umar got the first goal after 34 minutes and his namesake Aminu Umar doubled their lead two minutes into the second half.
Sadiq Umar scored his second and Nigeria's third seven minutes later when he controlled another good pass from their captain John Obi Mikel and hammered home from 15 yards (13.7m).
The goal appeared to have guaranteed victory but Honduras came back into the game and threated to win their first Olympic football medal.
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Antony Lozano got one back after 70 minutes when he headed home a cross from the right and then four minutes from time Marcelo Pereira rose among a pack of players to nod home a free kick.
But it was not quite enough and the Nigerians secured their first medal of the Rio games. Brazil take on Germany in the gold medal match later on Saturday.
(Editing by Nina Chestney)
