The 30-year-old striker, who was left out of Germany's World Cup-winning squad this summer, bagged a 31-minute hat-trick before adding two more to further torture Leverkusen's sixth-tier opponents.
Kiessling headed in from six yards on two minutes to start the rout, and doubled his tally as early as the 24th minute when he thrashed home from close range after a pass from Gonzalo Castro.
He secured the match ball seven minutes later by converting from Julian Brandt's through-ball, and made it four for him and Bayer prior to the interval when he tucked a penalty into the bottom corner.
Waldalgesheim, who play in the Verbandsliga Sudwest league, failed to register a shot on target and were five down when Kiessling completed his haul by firing in from Karim Bellarabi's layoff.
There was still time for Son Heung-Min to get on the scoresheet, striking low inside the post following a Sebastian Boenisch pass, as Bayer emphatically progressed to the last 16 of the competition.