In an untidy play-off, the two women hit a combined 87 unforced errors while Keys's challenge was undone by only converting two of her 10 break points.
Later Saturday, German second seed Angelique Kerber takes on Puerto Rico's Monica Puig for the gold medal.
Kerber is looking to become the second German winner of the title after Steffi Graf in 1988.
Puig bids to win Puerto Rico's first Olympic gold medal having already made sure of at least a silver.