The former West Brom and Nottingham Forest player appeared to provoke the PSG striker by bizarrely trying to insert his finger into the player's bottom with the referee not looking. Unsurprisingly, Cavani didn't take too kindly to the action, and flicked his hand in the fullback's face.
Jara, observing that the referee had seen the reaction, fell to the ground clutching his face, and the 28-year-old Uruguayan was dismissed despite the Chilean's role in the incident.
Chile went on grab a late winner through former QPR star Mauricio Isla, which saw Copa America holders Uruguay exiting the tournament.
And though Chile may have gone onto the next round, Jara's club future looks a little more bleak at Mainz. The Bundesliga side's sporting director Christian Heidel was massively critical of the player's actions following the game, telling Bild: "He knows that if an offer comes, he can go."
"We do not tolerate that. More than the prod, however, it is what comes afterwards that makes me angry. I hate theatrics more than anything."
Additionally, the player may end up being banned from the rest of Copa America for his antics
Jara featured in 20 games for Mainz last season after moving from the England, where he had played for West Brom for four seasons and Nottingham Forest for 18 months.