A tense contest at Villa Park was brought to life after 61 minutes when Kieran Richardson lashed home from the edge of the area, before the hosts levelled through on-loan striker Grant Holt nine minutes later.
Lewis Holtby went close to sealing a winner, but a combination of Matt Lowton's cross and an incredibly tight goal-decision system call denied the Tottenham loanee.
However, the win was sealed four minutes from time when substitute Hugo Rodallega rose to glance home the German's cross.
It was a noticeably resilient performance from Magath's men, one which delighted the former Wolfsburg boss and the travelling fans alike.
He told reporters after the game: "It was very important for us to win here after losing our last home game, so I think it was the last chance for us to stay in the league and therefore it was a very difficult game.
"We were one goal in front and then they got the equaliser - and that was the same situation that put us down last week, but today we came back and even missing the great chance Lewis Holtby had didn't stop us.
"I think that is a signal for everybody that we are back in the league."
Magath also singled out striker Rodallega for praise, with the long-suffering Colombian stating his claim for a place in the starting line-up with an accomplished performance.
"I was not always lucky with him over the last few weeks, but he's shown in the training stations that he is in good shape.
"I asked him before the game if he came in whether he would be in good shape and he said yes and said he would score.
"So I put him in the game."
The win lifts Fulham off the bottom of the table and five points adrift of 17th-placed Norwich, who travel to Craven Cottage next week.
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