Robin Dutt's Bremen have endured a miserable campaign to date and missed a chance to climb off the foot of the Bundesliga table as they slipped to their fifth defeat of the season.
After an uninspiring first half, the game briefly came to life after the interval and second-half substitute Ujah made an almost immediate impact by finding the net in the 59th minute.
The hosts came close to a swift equaliser when Izet Hajrovic struck the post from 25 yards, but Cologne held on to climb into the top half ahead of the weekend's action and increase the pressure on Dutt.
There was little action of note in a first half that saw Bremen's Zlatko Junuzovic booked for simulation after he went down in the area having not been touched.
Junuzovic came close to putting his side in front after the interval, but Timo Horn pulled off a fine save to keep out the Austrian's volley.
Ujah was introduced in the 58th minute and wasted little time in bringing a save from Raphael Wolf with a shot low to the goalkeeper's right.
The striker then scored from Cologne's next attack, sweeping home a first-time shot after Dusan Svento had got to the byline and pulled the ball back.
Hajrovic thumped a left-footed strike against the post as Bremen sought a response, but there was little thereafter to concern Cologne, who face another struggling side in Freiburg next weekend in the Bundesliga.
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