Kenya's world champion Julius Yego threw 88.24 metres on his first attempt, a season best and good enough to hold the lead until the penultimate round when Rohler unleashed his massive throw.
A limping Yego then retired from the competition having faulted on two of his previous throws.
London 2012 champion Keshorn Walcott of Trinidad and Tobago threw 85.38 metres on his second attempt. He needed a personal best on his last throw to bump Rohler from the gold medal position but produced a no throw and finished with bronze.
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Rohler has struggled with a back injury this season but showed promising form ahead of the Olympics, having thrown a world leading mark of 91.28 metres in June.
(Reporting by Jack Stubbs; Editing by Greg Stutchbury)
