The striker settled an entertaining contest in the 77th minute, finishing clinically past Marvin Schwabe after combining brilliantly with substitute Noel Aseko-Nkili.
The result was a welcome response from Frankfurt after their heavy 6-0 defeat by RB Leipzig, while Koln's miserable away record continued. They have now gone 16 Bundesliga away matches without a win, drawing six and losing 10.
Frankfurt started brightly at Deutsche Bank Park, but Koln also threatened in the opening exchanges. Noah Atubolu denied Marius Bulter early on before the hosts created several opportunities through Ebnoutalib and Fares Chaibi.
Koln goalkeeper Schwabe was kept busy, producing important saves to frustrate Frankfurt, while Atubolu also showed his quality by keeping out Bulter's first-time effort from a Borna Sosa free-kick.
Both teams continued to look for a breakthrough, with Koln's Said El Mala going close after a determined run, only to fire wide.
Frankfurt increased the pressure after half-time, with Ritsu Doan providing a dangerous attacking outlet. Schwabe produced another good save to deny Lilian Brassier's header before stopping Chaibi from close range.
Brassier later headed wide from a Chaibi corner as Frankfurt's frustration grew, but the home side finally found the decisive goal with 13 minutes remaining.
Aseko-Nkili provided the crucial assist, linking up with Ebnoutalib before the striker beat Schwabe at his near post with a precise right-footed finish.
The goal proved enough to secure three valuable points and lift Frankfurt back into the Bundesliga's top half.
Frankfurt coach Adi Hutter was delighted with the response from his players following their heavy defeat in Leipzig.
"Based on the second half, the victory is deserved," Hutter said. "The team showed a reaction and a different side after the 0-6 thrashing."
The coach also highlighted the importance of finally rewarding the home supporters with a victory.
"The 1-0 win is not only very important in this context, but also because it was our first home win in six months," he said.
Hutter praised the collective effort and singled out captain Robin Koch for special recognition after backing him following his difficult performance against Leipzig.
"Keeping a clean sheet is very important," he added. "I saw a team that ran together, supported each other, pushed each other, and fought. That's the most important thing."