The distance runner became the first British track and field athlete to win three Olympic golds as he came home in a time of 27:05.18.
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On the 10th lap, Farah tripped over USA runner Galen Rupp, his training partner.
“Mo Farah! The man with the plan!” tweeted Hollywood star Samuel L Jackson.
Rupp, the 2012 Olympic silver medalist, finished fifth.
Paul Tanui of Kenya was second with Tamirat Tola of Ethiopia coming in bronze medal position.
Farah started in his usual fashion, sitting at the back of the field for the first couple of laps, and it was only when he moved into the top 10 that trouble occurred.
He picked himself up, Rupp paced him back into the peleton, and from there Farah’s brilliance took over.
The 33-year-old was at the 3800m mark in the middle of the main pack when he accidentally kicked the back heel of a rival runner, sending him sprawling to the turf.
Farah then experienced a brief scare as he was inadvertently clipped by training partner Galen Rupp and fell to the track before quickly finding his feet and regathering his focus.
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But he brilliantly recovered to accumulate a second 10,000m title to add to the 5,000m gold he also won in London four years ago.
