The Swedes had scored only one goal in their last five internationals and it looked destined to be another goalless night for the Scandinavians until the Arsenal midfielder took advantage of a Marcus Allback header back across goal to send their desperate fans into ecstasy.
FC Copenhagen striker Allback had been called on at halftime by coach Lars Lagerback to replace the misfiring Zlatan Ibrahimovic and came close to scoring the winner on a number of occasions.
On the hour mark, he broke the offside trap and chipped the advancing Paraguayan keeper Aldo Bobadilla only to have defender Denis Caniza comes from the clouds to make a desperate save off the line.
20 minutes later, with his back to goal the 32 year old flicked on a Larsson header only to have the Libertad keeper again stop what seemed certain to be his 10th international goal.
The Paraguayans, the only team in Group B certain to depart the tournament after the group stages, had their chances but they were largely restricted to long range efforts.
Star striker Roque Santa Cruz, was largely anonymous and coach Anibal Ruiz rightly substituted him just after the hour.
The win sets up an intriguing fixture for the Swedes, who take on England with the winner topping the Group.
Should Lars Lagerback’s men fail to win they will be praying that Paraguay can at least draw with Trinidad and Tobago.
A dynamic start to the match failed to produce any goals in the first half.
Both sides were positive but lacked a cutting edge up front.
Sweden had the better of the half, their best chance a thunderbolt from Kim Kallstrom on nine minutes which needed the intervention of Bobodilla to stop it flying into the back of the net.