With just nine points from their first 17 games, the Bavarians had been written off by all but their most avid fans - and even Weinzierl himself.
But by taking 18 points in their last 13 matches, they are close to pulling off a minor miracle and proving the critics wrong, although Weinzierl has warned his team they still have work to do and must not fall short after coming so far in 2013.
Ahead of Saturday's contest with Stuttgart, the coach said: "Everybody here knows what this game means. We have four games to go and can reach our goal of staying up.
"For that, we need points. We had nine going into the winter break and practically everybody had written us off.
"Our aim back then was to keep things exciting right to the end and give ourselves a chance, and now we are precisely in the position we wanted to be in thanks to our good performances.
"But we want to carry it through to the conclusion."
Were the season to end now, Augsburg would face a play-off against the third strongest side in the 2.Bundesliga for a place in the top flight next season.
However, with just three points separating them from 15th-placed Fortuna Dusseldorf and safety, they may not even need that play-off to secure a third consecutive Bundesliga campaign.
"Everybody is motivated and we just have to infect everybody with our belief that we can achieve our biggest goal," Weinzierl said.
"The praise we have been receiving is not worth anything tomorrow [Saturday]. We have to perform, be decisive and get the points.
"That is all that counts."
Weinzierl is expected to name Ragnar Klavan in his defence in place of the suspended Kevin Vogt.
What he cannot expect is any gifts from a Stuttgart side who have already qualified for the Europa League by reaching the final of the DFB-Pokal, but who showed last weekend with a 2-1 win over Freiburg they are taking the end of the season seriously.
"We want to continue our upwards momentum," said coach Bruno Labbadia after a week which included three victories.
Labbadia is still without the injured Serdar Tasci but has otherwise vowed to name his "strongest side" for Saturday's encounter.