Trailing 1-0 from the first leg in Montevideo Australia levelled the play-off on aggregate through Marco Bresciano's first-half strike in a fiery match dominated by the hosts at Sydney's Telstra Stadium.
Although Mark Viduka missed a spot-kick the striker's Middlesbrough team-mate Schwarzer saved from Marcelo Zalayeta and Dario Rodriguez before John Aloisi tucked away Australia's fifth penalty to secure a famous win.
"He wasn't the only hero everyone involved in the team was brilliant said Neill who himself scored in the shoot-out. "Credit goes to everyone but Mark will take the plaudits and deservedly so."
Schwarzer said: "It's a huge wave of relief for everyone. When the game progressed we felt we had a good opportunity. They took off Recoba and (Paolo) Montero through injury so the sense of belief just mounted. Of the penalty shoot-out he added: "It was surreal I stood there and felt with every kick I knew where to go."
After a wait of 32 years since their only appearance at football's biggest tournament Australia held on in front of 82698 fans and took the game to penalties. Among the crowd was Hollywood actor John Travolta who celebrated with the Socceroos in the changing room after the dramatic finale. "Not only have we made the nation proud we had John Travolta in the changing room Neill added. "It's an amazing night and that capped it off."
Australia coach Guus Hiddink who is also in charge of Dutch side PSV Eindhoven now has the opportunity to enhance his FIFA World Cup pedigree after taking Korea Republic to the semi-finals in 2002. In a repeat of the play-off four years ago which Uruguay won comfortably the enterprise of Merseyside-based duo Tim Cahill and Harry Kewell gave Australia the upper hand.
Hiddink's side opened the scoring when Bresciano forced the ball home ten minutes from the interval. Cahill initiated the goal with a sharp turn before heading towards the penalty area and slipping the ball to Viduka. The big striker instinctively flicked towards Kewell who missed his shot before the ball fell invitingly for Bresciano to lash into the top corner.
The goal vindicated Hiddink's decision to bring on Kewell for centre-back Tony Popovic who had been cautioned shortly before for elbowing Uruguayan playmaker Alvaro Recoba.
"They made it very hard for us Neill said. "The 1-0 in the first leg was a good result and we put ourselves in a good position. We had the composure to keep the pressure on it went to the wire and was nerve-wracking but everyone got their value for money. Overall we've played fantastically well. There's a fantastic feeling in the changing room."
Uruguay coach Jorge Fossati who was missing striker Diego Forlan and veteran defender Diego Lopez said afterwards: "I feel great pain. I am at the lowest moment of my sporting life today. I am sorry to the Uruguayan public for failing at the last hurdle. I am at peace with myself. The players gave it their all. All of my players tonight fought like lions till the end."