But Alexander Meier pulled one back and then Marco Russ netted a dramatic 89th-minute equaliser.
Frankfurt enjoyed the better of the early exchanges without really testing home keeper Mathias Hain.
All Bielefeld could muster in the opening half hour was a 20-yard shot from Matthias Langkamp which drifted wide.
Hain was finally called into action after 32 minutes to keep out a Michael Thurk shot while Mehdi Mahdavikia was also denied three minutes before the break.
The deadlock was broken midway through the second period when good work from Wichniarek and Jorg Bohme resulted in the latter crossing for Kucera to head home from six yards.
Bielefeld doubled their advantage with 10 minutes to go, Christian Eigler crossing for Wichniarek to coolly slot home.
It appeared the home side were cruising to a comfortable victory but Frankfurt were not to be denied a share of the spoils.
They started their fightback when Meier took a pass from Albert Streit and cracked a shot past Hain.
And with nerves clearly in evidence in the home ranks, Frankfurt grabbed an equaliser when Russ slotted home from 20 yards.
Both sides have four points after solid starts to the new season.
Arminia Bielefeld 2 - Eintracht Frankfurt 2
1-0 Kuchera 68'
2-0 Wichniarek 80'
Frankfurt:(4-2-3-1) Proell-Kyrgiakos,Ochs,Russ,Spycher-Fink,Inamoto-Mahdavikia,Meier,Streit-Thurk