The Dusseldorf club are up to 13th on 18 points while Eintracht, with only one win in seven matches, are stuck in fifth spot on 24 points having set the best Bundesliga start by a promoted team with four successive victories.
The visitors had Karim Matmour sent off in the 34th minute for a second booking and four minutes later Stefan Reisinger put Fortuna in front, driving past two defenders to fire the ball in.
Promoted Fortuna made it 2-0 in the 42nd minute when Oliver Fink curled a 22-metre shot past keeper Kevin Trapp after shaking off two markers.
Nando Rafael, brought in to the team after Australian Robbie Kruse was injured in the warmup, was left completely unmarked in the box as he grabbed the third goal in the 58th minute.
Axel Bellinghausen sealed Fortuna's second successive home win five minutes from time, scoring through Trapp's legs.
Leaders Bayern Munich, 10 points clear on 37 points, host champions Borussia Dortmund on Saturday.