Darmstadt's late defeat dooms them to Bundesliga drop
Nikola Dovedan's injury time winner sealed Darmstadt's fate, leaving Torsten Lieberknecht's team 11 points adrift of possible safety with three games to play.
Darmstadt, who were relegated from the Bundesliga in 2017 and sealed a return to the top-flight last year, have won just three games all season and needed a victory on Sunday to keep their hopes of survival alive.
"It will take some time to process but we knew this day would come," Lieberknecht told DAZN.
"It's part of life as a sportsman, part of life as a footballer. The decisive factor is how we spend the next few days and weeks.
"The fans are naturally disappointed but they have shown that despite the disappointment everyone here is standing together and working together."
Earlier on Sunday, Cologne's Florian Kainz came off the bench to score a 95th minute penalty and salvage a 1-1 draw in Mainz.
Cologne remain second bottom and five points from the relegation play-off place that Mainz currently occupy but the last-gasp strike keeps Cologne's hopes of a miraculous escape alive and prevented Mainz climbing two places.
Mainz had appeared on course for a precious 1-0 win after Leandro Barreiro capped a swift counter-attack, scoring on a rebound after Cologne goalkeeper Marvin Schwaebe had thwarted Karim Onisiwo's initial effort.
Cologne spurned a golden opportunity to draw level 55 seconds after the restart when they were awarded a penalty for Frenchman Anthony Caci's clumsy challenge on Faride Alidou – but Luca Waldschmidt put the spot-kick wide.
But Cologne won a second penalty four minutes into stoppage time after a VAR check confirmed a foul by the Mainz goalkeeper Robin Zentner. Kainz kept his cool, sending Zentner the wrong way.
A late straight red card for Mainz's Philipp Mwene soured things further for the hosts, who are now points behind Bochum and Union Berlin.
Union had played out a 0-0 draw at Borussia Moenchengladbach earlier on Sunday, collecting only their second point since their last league win, on March 30th.
Union have scored only once in their last five games and face back-to-back six-pointers, first next Sunday against Bochum and then against Cologne.
Moenchengladbach are still in danger, with only a two-point cushion on the two teams below them. The Foals have won just one of their last eight league games.