The Group A clash never reached any great heights at the Camping World Stadium in Orlando, Florida as the teams shared the spoils in warm conditions.
Jorge Benitez had the best chance of the game early on, but his poor attempt at a finish illustrated the struggles of both sides.
With men behind the ball throughout, Costa Rica were left to try and make the most of set-pieces and Bryan Ruiz's first-half header was as close as they got.
Costa Rica were reduced to 10 men in additional time as Kendall Waston was sent off for a crude late challenge.
A draw always looked the most likely result as the teams were left behind Colombia, who had a tournament-opening win over hosts the United States.
Ramon Diaz made three changes to the Paraguay team beaten by Mexico, with Fabian Balbuena, Blas Riveros and Antonio Sanabria making way for Miguel Samudio, Gustavo Gomez and Dario Lezcano.
One of Costa Rica's two inclusions – Yeltsin Tejeda – made his presence felt immediately, picking up a yellow card for a rash sliding challenge inside 20 seconds.
Oscar Ramirez is without goalkeeper Keylor Navas, the Real Madrid shot-stopper having suffered an Achilles injury to rule him out of the tournament.
Paraguay controlled the opening exchanges and should have made the most of their dominance in the 13th minute.
Benitez was played in behind by Derlis Gonzalez, but the Cruz Azul forward scuffed his shot across the face of goal.
Paulo da Silva headed a great chance just wide from the resulting corner.
Costa Rica almost made Paraguay pay for the misses as Joel Campbell picked out Ruiz with a set-piece, but the captain's header was straight at Justo Villar.
While Diaz's men looked the more likely, Costa Rica settled into the encounter as the half wore on.
Neither team was able to penetrate to start the second half, with Bruno Valdez threatening for Paraguay – but he was unable to get enough on a 71st-minute corner.
A scuffle in the dying stages brought some much-needed life to the encounter and substitute Cristian Bolanos forced a save out of Villar in the 88th minute before Waston was red-carded for a late challenge on Nelson Valdez.