A year ago, Augsburg were in a similarly precarious position, but 23 points in the second half of the season saw them avoid relegation by eight points, despite occupying a place in the bottom three at the turn of the year.
Meier expects a similar Augsburg revival in 2013, which is why his side have got to be on guard at the Dusseldorf Arena on Sunday.
"We have a very important game straight away against Augsburg," he said.
"The difference between the two sides in terms of points is misleading. Augsburg impressed in earning a second season in the Bundesliga last year.
"This is a game between two sides on a par with each other, as we saw in the reverse fixture."
Parity is a long way from being established in terms of points, though, and that could be rendered even more unlikely with a home win, which would leave Augsburg in serious danger and give Fortuna more than just a bit of breathing space.
"A positive result would also be great as it would boost our self-confidence," added Meier at a press conference.
New signings Martin Latka and Robert Tesche are both candidates for a place in the Fortuna squad.
Augsburg also had a new arrival during the winter break with Stefan Reuter lending his support to coach Markus Weinzierl as the club's new director of sport.
And they swelled the ranks further with a new player who may well have been bought with just Sunday's game in mind.
"He knows how to beat Dusseldorf," said Reuter of 22-year-old midfielder Andre Hahn, who has joined from Kickers Ofenbach, the side which knocked Fortuna out of the DFB-Pokal this season.
"Andre's good performances for Offenbach brought him to our attention and he can definitely help us," added Weinzierl.
Augsburg will be without Aristide Bance for the next few weeks as he is currently on international duty with Burkina Faso at the African Nations Cup.