A minute later Sebastian Boenisch put Bayer in the lead, firing home from close range.
It became 2-0 to the home side on 33 minutes when Stefan Kiessling latched on to Castro's pass and found the target from close range.
Bayer continued to dominate the contest in the second half and scored their third goal on 58 minutes, Andre Schurrle shooting home from the right side of the Eintracht penalty area after being released by Kiessling.
Eintracht were unlucky not to pull one back midway through the second half when Olivier Occean saw his close-range header come off the post.
Ten minutes later Alexander Meier did score for the visitors from close range, but it proved to be too little, too late.