The French striker struck in the 63rd minute to cut the deficit and then levelled with his 82nd-minute header to earn a surprise point for the hosts.
Jeremie Frimpong came close to adding a third when his effort hit the crossbar in the 25th as the visitors looked to be cruising to a comfortable win in the local derby.
But Modeste first made the most of some bad defending from Jonathan Tah to pull a goal back and then completed the turnaround with a header that wrongfooted keeper Lukas Hradecky after some more sloppy defending.
There was more bad news for Leverkusen with their top striker Schick getting helped off the pitch with an injury with minutes left to play.
The result means Leverkusen drop to fourth place on 17 points, five off leaders Bayern Munich. Cologne are eighth on 13.