But despite opening the scoring with a 39th minute header from Antolin Alcaraz, Paraguay made repeated errors in set pieces, squandering chances and gifting Italy their equaliser.
"It was a very tough opening game. We made a great start but we made mistakes in set pieces ... there were lapses of concentration which we can't afford to let happen," said forward Roque Santa Cruz, something of a surprise exclusion from the starting team but who came on in the 69th minute.
"I don't think we played out best football. We need to improve our set pieces...Italy didn't have a lot of chances. They only scored from a set piece," he added.
Italy levelled in the 63rd minute when a Simone Pepe corner sailed past goalkeeper Justo Villar's flailing fist and Daniele De Rossi stuck out a foot to steer the ball into the empty net.
With a valuable point from the game, buoyant Paraguay play Slovakia next on June 20 followed by New Zealand on June 24.
"We've just played the world champions and we've come away with a draw. It has given us a lot of confidence," said striker Lucas Barrios.
"We wanted to play at the same level as Italy, we didn't want to just defend. So we're happy even though we could have won the game."
However, he acknowledged Paraguay would need to be a lot more clinical in front of goal to secure a qualifying berth.
"I think the next games will be much more open and they should be a bit easier for us. We'll need to work on how we convert and on our precision," Barrios said.
The South Americans have never gone beyond the second round in the finals before but progressing to the next phase is their minimum target.
"We want to go at least to the quarter-finals because in Paraguayan history it's never been done," said Santa Cruz.
Coach Gerardo Martino is likely to leave Slovakia guessing as to the strikers he will field, after both Lucas Barrios and Nelson Valdez were replaced during the Italy encounter. "I was not really 100 percent. I had a muscle problem and didn't know if I could play from the beginning, so I think the coach took the best solution and the right choice," Santa Cruz said.
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