Luka Jovic started for the hosts, with the 21-year-old Serbia hitman boasting 26 goals for club and country this term.
And Jovic continued his fine season with his 27th goal in all competitions for club and country to put Frankfurt 1-0 against Chelsea after flicking a header in off the far post.
Chelsea responded in Germany with strikes from Pedro and Willian, but both efforts were wide of the target.
Ruben Loftus-Cheek was inches from equalising for Chelsea when he rattled the post as the visitors began to gain a foothold in the match.
And Maurizio Sarri’s side grabbed a leveller on the stroke of half-time through Pedro, who had space in the box to drill a fierce low effort into the bottom corner.
Loftus-Cheek spurned another great opportunity to get on the scoresheet when he linked up with Pedro but could not keep his effort down.