Cologne beat Bayern 2-1 last weekend and Friday's draw gave Christoph Daum's team 29 points after 22 rounds for 10th place.
"We wanted to win this game but Bielefeld played really tough and in the end I think we have to be satisfied with the point," Daum said.
Bielefeld earned a valuable point on the road for 20 points, two points above the drop zone.
Cologne grabbed the lead after 15 minutes on a fine header from near the post by captain Petit.
The host was unable to capitalize on a couple of other chances before Bielefeld pushed forward looking for the equalizer.
Bielefeld knotted the score in the 43rd after a mistake in defense. Miso Brecko's back pass to Cologne goalkeeper Faryd Mondragon bounced off Pedro Geromel and Katongo struck the loose ball into the right corner from 22 meters.
Bielefeld was happy with the point and focused on its defense though Cologne had the better chances the rest of the way.
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