But a last-ditch cross from Johan Elmander, a delicate nod back across goal from Marcus Allbäck and a pinpoint header by Ljungberg sent 40,000 Swedes in Berlin’s Olympic Stadium into raptures.
Sweden now face compatriot Sven-Göran Eriksson’s England on Tuesday as they bid to win Group B with either hosts Germany or Ecuador waiting in the next round.
England are certain of their place while the Swedes can still mathematically be caught by Trinidad and Tobago.
Despite having the lion’s share of the possession the Swedes were unable to force an early breakthrough despite the probings of Juventus playmaker Zlatan Ibrahimovic, whose failure to find his usual lustre saw him replaced at the break by Marcus Allback.
Roberto Acuna welcomed the Copenhagen striker by felling him to pick up a booking as the Paraguayans offered a muscular approach.
But just when it looked as if a goalless draw that would have suited neither side was set to be the end product Ljungberg nodded home after Allbäck headed across goal to find the midfielder lurking on the edge of the six-yard box.
The goal sparked bedlam on the Swedish bench and among some 40,000 Swedish fans inside the Olympic Stadium.
With England having made it into the last 16 by virtue of a laboured 2-0 win against minnows Trinidad and Tobago, the Swedes, who could only draw against the Caribbean side in their opener, were seeking to move onto four points.
And they just made it.
Sweden were hoping their forward line of Henrik Larsson, Ibrahimovic and Ljungberg would see them home and dry but they were foundering on a rocklike back four relentlessly held together by Paraguayan skipper Carlos Gamarra, whose own goal handed England their narrow win in Frankfurt.
Sweden’s early best chance fell to Kim Källström, who forced Aldo Bobadilla to make a two-handed stop on nine minutes in goal with a piledriver.
Christian Wilhelmsson then went close after good work by Ljungberg.
The Paraguayans, industrious but at times over physical, had few good chances and Nelson Valdez wasted one in firing well over from a Santa Cruz knockdown midway through the opening period.
Sweden made two changes from the side which could not break down Trinidad and Tobago with Andreas Isaksson in goal in place of Rami Shaaban and Anders Svensson stepping down for Kim Källström in midfield.
The Swedish midfielder produced the first quality effort of the encounter, a meaty 25-metre drive which forced a two-handed save from Bobadilla.
Valdez shot into the side netting and a speculative Carlos Bonet effort flew too high as the Paraguayans clearly decided they had to up the pace after the break and Acuna then sent a low effort too close to Isaksson.
On the hour mark Sweden came within centimetres of scoring when Allbäck tried to lob Bobadilla only for Caniza to get back and hack clear, the defender ending up in the back of the net.
Paraguay reacted as Dante Lopez came on for the ineffective Roque Santa Cruz.
Larsson went close with a header over as the Swedes enjoyed another purple patch and then the veteran did his best to gift Allback another chance but Bobadilla clutched the striker’s acrobatic flick.
“I think we played pretty well, better than against Trinidad and Tobago. We had a little more patience. Our passing game was faster and simpler,” said a beaming Ljungberg after the game.
“And the crowd was unbelievable, screaming like mad. It was a fantastic experience.”
Sweden will play England next Tuesday and a draw will ensure that Lars Lagerbäck’s team progress to the next stage.