Korkut's men came through an enthralling encounter 3-2 at the Commerzbank-Arena, with four of the goals coming in the opening half an hour.
While Alexander Meier pulled a second goal back for Frankfurt after the break, it failed to spark a comeback for the hosts as Korkut's side moved up to 12th - eight points off the relegation zone.
With three games remaining, Korku has warned his players that their Bundesliga status is not yet assured.
"That was a very, very important win for us but mathematically we are still not safe," he said in quotes reported by Kicker.
"The team has won and it was richly deserved. I am proud to be coach of such a team."
Frankfurt coach Armin Veh said he always felt the fixture was likely to cause his side problems and voiced his frustration at the result.
"I had a bad feeling before the game," he said.
"We played as if we were already safe. I said before the last game that we are not safe but I was the only voice in the wilderness."
