Magath celebrated his first away win since taking charge of the Cottagers as goals from Kieran Richardson and Hugo Rodallega earned them a 2-1 triumph at Villa Park.
Fulham remain five points adrift of safety with five games remaining after West Brom and Crystal Palace also won, but Magath believes the victory will give them impetus for their survival push.
He said: "It was very important we won here after losing our last home game
I think today was our last chance for us to stay in the league
Therefore, it was a very difficult game and very spectacular
"We were one goal in front, there was an equaliser, and that was the situation last week that put us down
Today we came back and we fought.
"Even the great chance for Lewis Holtby didn't stop us
For us to win in the last five minutes is a signal to everybody that we are back in the league
Everyone at the game could see we want to stay in this league
"We have to win our games now
It doesn't matter which team we play
We need to win three of the last games at least to stay in the league
We will fight every game
Today we have won and this win will give us confidence."
There was a feeling after Fulham's home defeat by Everton last weekend that they were virtually condemned to life in the Championship.
But they received vociferous support from their travelling fans at Villa Park and took the lead in the 61st minute when Richardson rifled in a shot from outside the area.
It was a very open game, and it took Villa only nine minutes to find an equaliser as Grant Holt headed in his first goal for the club.
Fulham looked certain to retake the lead when Lewis Holtby rounded Brad Guzan only to see Matthew Lowton pull off a miraculous clearance with virtually the whole of the ball over the line.
But the visitors were not to be denied and in the 86th minute half-time substitute Rodallega flicked Holtby's cross into the bottom corner.
Magath revealed he has given his players two days off as a reward, saying: "You can imagine now how the players in the locker room are happy, happy and they forced me to give them two days off, so I have
They deserved it today."
Fulham's happiness was Villa's despair, with Paul Lambert's side left looking nervously over their shoulders again after a third straight defeat
Lambert was left with little choice but to play Holt up front after the blow of Christian Benteke being ruled out for the season with a torn Achilles, while Gabriel Agbonlahor failed to recover from a stomach bug
Villa were also without key midfielder Fabian Delph after he picked up an injury
Lambert said: "We lost Fabian this morning and Gabby hadn't recovered from the bug and throw (Karim) El Ahmadi into it - that's a big chunk of our team
"Looking at the table and fixtures, there are some real hard games for everyone
You have to go and get over that line as quickly as you can
"I'd rather be in our position than a lot of teams
You have to look after yourself."