After a heated start, it was Paraguay that came closest to breaking the game's deadlock, as Nestor Ortigoza's delivery into the box was met by Nelson Valdez, who headed towards the back post, with Barrios only inches away from making it 1-0.
However, it was Uruguay that opened the scoring when a Carlos Sanchez delivery was met by the head of Gimenez, who managed to get between two defenders to make it 1-0.
Uruguay had a couple more chances to extend their lead before half time, as efforts from Gimenez and Edinson Cavani were unable to beat the Paraguayan goalkeeper.
However, it was La Celeste who were left ruing their missed efforts, as Barrios's powerful header was too much for the Uruguayan goalkeeper, putting the score level seconds before the interval.
The second half failed to produce much of the same action as the first, with only one game-winning chance coming in stoppage time.
In the dying seconds, Derlis Gonzalez slipped in Roque Santa Cruz on the edge of the box, with the striker drilling his effort towards the bottom corner of the Uruguay goal, only for Fernando Muslera to deny the former Blackburn Rovers forward with a fine save to keep the scores level.
The point sends Uruguay through to the knockout stages of the competition while Paraguay sit third in Group C on four points.