Hamilton midfielder Ali Crawford made the breakthrough four minutes into the second half after the Celtic defence failed to deal with a Stephen Hendrie cross into the box.
Celtic squandered a number of chances to equalise as manager Ronny Deila, who has struggled since taking over from Neil Lennon during the close season, was booed at the final whistle.
Table-toppers Hamilton, who were promoted from the Scottish Championship (second tier) last season, have 20 points from nine games, while Celtic are sixth with 14 points from eight matches.
(Reporting By Michael Hann, editing by Pritha Sarkar)
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