Dutchman Klaas-Jan Huntelaar struck twice as Schalke took up their last chance of a European place after a rollercoaster season saw them reach the Champions League semi-finals but finish 14th in the Bundesliga.
It was the highest winning margin in the German Cup final since Schalke's 5-0 win over Kaiserslautern in 1972 and the first time striker Raul had won a domestic cup, failing to triumph in the Spanish version during 16 years at Real Madrid.
"We were very concentrated from the start and it turned out to be a clear win, thank God," Schalke coach Ralf Rangnick, who took over from Felix Magath in mid-March, told reporters.
Teenager Julian Draxler fired them into the lead on 18 minutes after a well-timed pass from Peruvian Jefferson Farfan, who four minutes later set up Huntelaar for the second with injury-plagued Duisburg missing half a dozen key players.
Farfan then sent in a corner for Benedikt Hoewedes to head home after 42 minutes, putting the game beyond Duisburg.
Huntelaar turned provider early in the second half, slicing the defense open yet again for Jurado to score, before the former Real Madrid and AC Milan forward added another himself after a defensive blunder.
"To end a season of such highs and lows with a trophy obviously feels very good," said Schalke sports director Horst Heldt. "We are proud of this team." Germany goalkeeper Neuer had little to do as Schalke gave the Zebras no real chance, pouring forward from the start in front of 75,000 fans at Berlin's Olympic stadium.
Schalke captain Neuer, who lifted his first major trophy to kick off wild celebrations amid 30,000 traveling fans, looks close to a deal with Bayern Munich after saying he would not extend his contract with his boyhood club past 2012.
"This is a dream," Neuer said after receiving the cup from German President Christian Wulff, flanked by national coach Joachim Loew.
"I am enjoying every moment of it because for me a dream is fulfilled," added the 25-year-old.
However, he did not say if or when he would join Bayern.
"This is something I cannot say at the moment because this depends on those responsible. I cannot say when it will be announced because I do not know," he told Sky Television.
For Duisburg it was their fourth defeat in four finals.
"We are a bit disappointed because we did not get what we wanted but my players were winners even before the game," said Duisburg coach Milan Sasic.
