Farah tumbled to the ground after appearing to trip over American Galen Rupp on the 10th lap at the Olympic Stadium on Saturday, reports Xinhua.
But he recovered quickly to set the pace before charging to the finish line in a time of 27 minutes 5.17 seconds.
Kenya's Paulo Tanui took silver in 27:05.64 and Ethiopia's Tamirat Tola grabbed bronze in 27:06.26.
Farah is the first Briton to claim three gold medals in athletics at the Olympic Games.
The 33-year-old won the 5,000m and 10,000m at the 2012 London Games.
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