Eintracht's Alexander Meier needed less than a minute to score his seventh goal of the season, drilling in a low shot from 14 metres after Fuerth failed to clear the first attack of the game.
The visitors quickly shrugged off the early setback but veteran forward Gerald Asamoah wasted two golden opportunities to level from point-blank range.
Fuerth earned the deserved equaliser in the 53rd minute with Zoltan Stieber wrapping up a textbook break with an audacious left-footed chip over keeper Kevin Trapp as the visitors took control.
Eintracht had Trapp to thank for rescuing a point with a string of superb saves late in the second half with Fuerth brimming with confidence.
The draw was enough to lift Fuerth off last place and stretch their unbeaten run to three games as they gradually adapt to life in the top flight.
Leaders Bayern, on 24 points, travel to Hamburg SV on Saturday while fourth-placed champions Borussia Dortmund, on 15, host in-form VfB Stuttgart.
Fellow Champions League competitors Schalke 04, in second place on 20 like Frankfurt, visit Hoffenheim.
- Sports & Recreation
- Alexander Meier
- Gerald Asamoah