The Ghana international netted the winner in the 26th minute to wrap up the game early at Commerzbank-Arena.
It was the 30-year-old's fifth league goal of the season, having made 23 appearances involving 20 starts.
Frankfurt, however, were not in the driving seat from the get-go of Monday's fixture.
Jean-Kevin Augustin put the away side in front in the 13th minute with a shot into the corner after being set up by Konrad Laimer.
Timothy Chandler then hit back for Frankfurt nine minutes later, poking home from close range on the assist of David Angel Abraham.
Shortly, Boateng wrapped up three points for the home side, slotting Ante Rebic's cross into the net.
The Eagles have, thus, moved closer to second-placed Borussia Dortmund on the league table, only separated by a point.
For their next game, Niko Kovac's men play away to VfB Stuttgart on Saturday.