France beat hosts Japan 4-1 in the final, with Clarisse Agbegnenou earning a second gold at the Games, and Axel Clerget, Guillaume Chaine, Sarah Leonie Cysique and Romane Diko the other team members along with Riner.
Bronze medals went to Israel and Germany.
Riner, 32, also won +100kg bronze on Friday, to go with double gold from 2012 and 2016 plus a first bronze in 2008.
No other man has won five medals in the sport but Japan's Ryoko Tani has achieved it on the women's side with a 2-2-1 haul between 1992 and 2008.
The mixed event completed the Olympic judo action in the iconic Budokan arena where hosts Japan led the way with a 9-2-1 medal count from 15 events, and France a distant second on 2-3-3.
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