Australia will head to Dallas to face the Group G runners-up - either Belgium, Egypt, Iran or New Zealand on July 1 - after finishing second in Group D with the stalemate at Levi's Stadium.
The Socceroos finished on four points, behind the US (six) and ahead of Paraguay (four) on goal difference, with last-placed Turkey (three) eliminated.
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."
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.
"It's a special day," Popovic said in his press conference.
"We've seen already how many big nations have not gone through - it's the World Cup, it's difficult.
"You play different styles from different countries. We've done it now twice consecutively.
"So a wonderful achievement in Qatar. We've backed it up again, and we have a chance to go further in and maybe do something even more 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.
Friday's matches between New Zealand (one point) and Belgium (two), plus Egypt (four) and Iran (two) will determine Australia's next opponents.
Man of the match Aiden O'Neill said: "It's huge. I think coming into the World Cup, not many people gave us a chance to come second in the group and that's the belief that we have in our squad".
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, but wouldn't go into why he made his changes.
The magnificent Jordan Bos was aggressive and dynamic as Jacob Italiano's replacement at right wing-back, with Behich starting on the left.
"It's the best game he's played of the three by far," Popovic said of Bos.
In his first start this tournament, Irvine was imperious in midfield alongside O'Neill.
"It was nice to see Jackson today because that's the Jackson that I remember," Popovic said.
Herrington, Australia's youngest ever World Cup starter on his tournament debut, was unflappable in defence, with Popovic labelling the 18-year-old "outstanding".
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.
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.
