Simon Makienok, who had initially been left on the bench before coming on at half-time, equalised around nine minutes before the break with a towering header. He could have won it late on, but only hit the side netting from a great position.
Fürth had taken the lead early with Daniel Keita-Ruel heading in a cross put in by Maximilian Wittek. Former Dresden man Marvin Stefaniak also hit the post as the Kleeblatt dominated the first half.
Dresden improved after Markus Kauczinski switched from his initially 3-4-3 to 4-4-2 at the break, with Makienok joining Alexander Jeremejeff up front. The latter headed wide before his Danish strike partner brought the sides level.
With just one game left in hand now, Dresden are level on points with SV Wehen Wiesbaden, whom they beat at the weekend, but remain behind them on goal difference. They are two points behind Karlsruher SC in 16th, but still five points from complete safety, with 1. FC Nürnberg currently 15th. They play Hamburger SV next on Friday.
The draw means Fürth remain without a win since the coronavirus break but they join the teams on 39 points who are probably safe from relegation. A relief ahead of the derby against Nürnberg at the weekend.
Dresden: Broll; Ehlers, Ballas, Müller (Makienok HT); Wahlqvist (Kreuzer 62‘), Petrak, Nikoalou, Hamalainen; Horvath, Jeremejeff (Königsdörffer 90+1‘), Terrazzino (C. Löwe 71‘).
Fürth: Burchert; Meyerhöfer, Jaeckel, Bauer, Wittek; Sarpei, Seguin (Green 76‘), Ernst (Mavraj 88‘); Hrgota (Tillman 76‘), Keita-Ruel (Nielsen 57‘), Stefaniak (Leweling 57‘).
Goals: Makienok (54‘); Keita-Ruel (13‘).
Referee: Christof Günsch.