Marco Russ scored the only goal on the hour mark but Frankfurt were indebted to goalkeeper Kevin Trapp for preserving their advantage until the whistle.
Joselu missed a penalty that would have made it 2-0 deep in stoppage time but Frankfurt held on to move three points clear of the relegation zone, while leaving Leverkusen seven adrift of Bayern Munich at the top of the table.
In Sunday’s other game, Schalke overcame Freiburg 2-0 to move back up to sixth.
An unfortunate Nicolas Hofler own goal gave the hosts the lead before a Jefferson Farfan penalty made sure of victory for the Royal Blues, who reached the last 16 of the Champions League on Wednesday.
The game also marked the return to action of former Liverpool target Kyriakos Papadopoulos after over a year out with a knee injury.