Kevin-Prince Boateng put the hosts ahead in the 43rd minute and Luka Jovic scored in second-half stoppage-time to lift Frankfurt, with two wins and a draw since the Bundesliga resumed after the winter break earlier this month, to 33 points.
They are two points ahead of Gladbach as well as Bayer Leverkusen, Schalke and RB Leipzig who are in action over the weekend.
Frankfurt went ahead at the end of a lacklustre first half with Boateng's close-range effort.
They then had to endure Gladbach pressure for much of the second half but hung on for the win.
The visitors could have equalised when Boateng brought down Lars Stindl in the box but instead Thorgan Hazard thundered his 78th-minute penalty onto the crossbar, his first miss this season after converting his previous four spot kicks.
Jovic then struck late to make sure of the three points.
Bayern Munich, top on 47 points, host Hoffenheim on Saturday afternoon (Sunday morning AEDT).
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