The win, only their second of the season, lifted Augsburg to within a point of the relegation play-off and, although they are still nine points away from guaranteed safety, Weinzierl is confident they can repeat their climb up the table in the second half of last season and book a third campaign in the top flight.
"Whoever has already written us off has made a mistake," he said.
"We dominated for 45 minutes and deserved to take the lead.
"Leading 3-0 should really have given us self confidence, but Dusseldorf came back into the game.
"That got us thinking and, in the end, we had the necessary luck to hold on, but we can take heart from our performance before the break."
Sascha Molders was Augsburg's hero with two goals on a day when the club announced he had extended his contract until 2015.
"We desperately wanted this win and you could see that," he said.
"Augsburg are back."
While Augsburg are battling for survival, Fortuna need to keep a close eye on what is developing below them with their top-flight status far from secure.
"I said before the game that it was a game between two evenly matched sides and, often in games like these, mistakes make the difference, and we committed two enormous blunders," said Fortuna coach Norbert Meier.