Koji Miyoshi gave the tournament guests the lead in the 25th minute with a confident finish following a counterattack but Luis Suarez levelled seven minutes later from the penalty spot after a controversial decision following a VAR review.
Japan defender Naomichi Ueda, who appeared to be kicked by Edinson Cavani in a dispute for the ball, was penalised to the bemusement of the Asian side.
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They restored their lead in the 59th minute when Miyoshi pounced on an error by Uruguay keeper Fernando Muslera to score his second of the game.
The 15-time Copa America champions equalised again seven minutes later through a header from defender Jose Gimenez.
Uruguay lead Group C with four points, while Japan are third with one.
Second-placed Chile meet bottom side Ecuador on Friday evening before the final round of Group C matches take place on Monday 24 June.
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