Emmanuel Iyoha and Lion Lauberbach scored in each half, with Dresden reduced to ten men after Jannik Müller saw two quick-fire yellow cards.
Markus Kauczinski’s side are now five points adrift of Karlsruher SC in 16th and must win both of their remaining games to have any chance of reaching the play-off place. Kiel’s safety, whilst never really in doubt, is now secure.
Kiel were without coach Ole Werner and had failed to win any of their four previous games but they had few problems against a Dresden side playing their seventh game in 18 days and looking mentally shot.
Dresden had competed well in the early stages with Ondrej Petrák capitalising on a Jonas Meffert mistake but seeing his shot saved by Ioannis Gelios. The Kiel goalkeeper also reacted well to a Chris Löwe free-kick.
Fabian Reese and Lee Jae-song had chances for the hosts, but the game turned firmly in their favour when Müller saw his second card in four minutes for a foul on Jannik Dehm. Shortly after, Iyoha opened the scoring, cutting in from the left and beating Kevin Broll with a good finish.
The Storks continued to dominate with the man advantage in the second half, and they made it count ten minutes from time, when substitutes David Atanga and Lauberbach combined to capitalise on a mistake on the ball from Kevin Ehlers.
Alexander Jeremejeff thought he had pulled one back late on, only for it to be disallowed for a tight, but correct, offside decision. Lauberbach was denied his second and Kiel’s third by Broll, solid as ever in Dresden’s goal, in stoppage time.
Kiel: Gelios; Dehm, Wahl, Thesker, van den Bergh; Meffert, Porath (Sander 84‘), Özcan; Reese (Atanga 74‘), Lee (Lauberbach 60‘), Iyoha.
Dresden: Broll; Kreuzer, Ballas, Müller, C. Löwe; Petrák (Donyoh 84‘), Hušbauer (Ehlers HT); Schmidt (Terrazzino 57‘), Klingenburg (Ebert HT), Horvath; Makienok (Jeremejeff 57‘).
Goals: Iyoha (45+1‘), Lauberbach (80′).
Referee: Patrick Ittrich.