Antolin Alcaraz thumped in a header after 39 minutes as the world champions more than lived up to their reputation as slow starters, delivering a damp squib of a display perfectly suited to cold and miserable Cape Town weather.
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The Italians were slightly better in the second half, levelling after another goalkeeping blunder in the 63rd minute, but did precious little to change the pessimistic view of their fans and media who sent them to South Africa amid widespread predictions of an early return.
Italy coach Marcello Lippi, who had said on Sunday that a draw would not be a disaster, told reporters: "I'm very satisfied with our performance, I'm very satisfied with the approach to the World Cup.
"The first time they got near goal they scored, then there was a good reaction from us and we equalised. But we created little danger for the amount of possession we had."
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Paraguay, who had beaten Brazil and Argentina in qualifying, had no need to be in fear of the holders but their dire World Cup record where they have not got past the second round in seven attempts, going out in the group stage four times, was always there in the background.
Nevertheless, they settled well and produced a hugely disciplined and hard-working display to keep the Italians largely beyond the penalty area.
The game had meandered through almost an entire half of error-littered, unimaginative play before exploding into life in the 39th minute.
Aureliano Torres swung in a hopeful free kick from wide on the right but Alcaraz showed great determination to make it his, rising early and high above Fabio Cannavaro to power his header beyond Gianluigi Buffon.
It was a stunning blow for the Italians, who had looked completely untroubled until that point, albeit without ever looking remotely like scoring themselves.
The holders were forced to bring on substitute goalkeeper Federico Marchetti at half time after Buffon hurt his back but, with key creative midfielder Andrea Pirlo absent through injury, it was at the other end of the pitch where they needed inspiration.
Little was forthcoming but they levelled when Justo Villar flapped at and missed a Simone Pepe corner and De Rossi stuck out a foot to steer the ball into the empty net.
Italy roused themselves in the last 10 minutes in search of a winner but stout defending saw Paraguay hold on for deserved point.
Lippi's team, who face New Zealand and Slovakia in their remaining group games, will look to 1982 for inspiration, when they drew their opener but went on to win the tournament.
