Australia will head to Dallas to face the Group G runners-up - either Belgium, Egypt, Iran or New Zealand - after finishing second in Group D.
The Socceroos needed a win or draw in Santa Clara on Thursday (Friday AEST), while Paraguay (four points) should be one of the best third-placed finishers to also progress ahead of Turkey.
In finishing second, rather than third, Australia also avoid a do-or-die match-up with heavyweights Germany or France.
"Just unbelievable, unbelievable. Just so proud of everyone involved - the staff, the players, just a wonderful young group of men," jubilant coach Tony Popovic told SBS.
"Now we go to Dallas and we'll try and do something special."
Popovic was rewarded for bold selection calls, which included starting Nestory Irankunda and Cristian Volpato - and six total changes to the line-up that lost 2-0 to the United States.
Australia dominated but could not find their way through a tenacious Paraguay defence, but won't care after reaching the knockouts at back-to-back World Cups for the first time.
The Socceroos will eagerly await Friday's matches between New Zealand (one point) and Belgium (two), plus Egypt (four) and Iran (two) that will determine their next opponents.
Popovic added earning an extra day's rest before their next game was also crucial.
"It's important for us. These boys are building. They're trying to get fitter and stronger and the eight days gives us a chance to recover properly, get them all healthy, strong, available, and ready for the next challenge," he said.
Popovic called upon Irankunda, Volpato, Connor Metcalfe, Lucas Herrington, Jackson Irvine and Aziz Behich.
Australia were on top early, dominating possession, with the magnificent Jordan Bos aggressive and dynamic as Jacob Italiano's replacement at right wing-back, with Behich starting on the left.
Irvine was imperious in midfield alongside Aiden O'Neill, strong on the ball and in the air, while Herrington, Australia's youngest ever World Cup starter on his tournament debut, was unflappable in defence.
In 58 minutes, Volpato was exciting, linking up with Bos on the right, breaking into little pockets and troubling Paraguay's defence.
Irankunda, who replaced Mohamed Toure, toiled hard as a back-to-goal striker and caused flashes of chaos.
In the fourth minute, Bos found Volpato who cut back for Irvine to force a save from Orlando Gill at his near post.
Volpato went on a wonderful run into the box in the 12th and arguably could have gone down under contact, while he teed up Bos for a shot that was saved in the 36th.
In first-half added time, Bos found Volpato on the overlap and the winger cut onto his left and forced a save.
Irankunda wanted a penalty in the 49th minute, but it wasn't forthcoming.
Paraguay had their first shot on target a minute later through Mauricio, but Patrick Beach comfortably claimed it.
Bos made terrific runs into the box in the 83rd and 90th minutes, but fired one straight at the South Americans' goalkeeper and the other wide.
Stressing out Popovic, Mauricio forced Beach into an added-time save.
"The one at the end was the first time that I really looked at the clock and thought, 'Please, blow the whistle'. But I think overall we deserved it," Popovic said.
"We were very good today. Just a wonderful performance."
Tete Yengi was denied a chance to be Australia's hero at the death, but it didn't matter as Socceroos fans around the globe rejoiced.
