Kiessling's brace leads Leverkusen
Pierre-Emerick Aubameyang and Robert Lewandowski grabbed a brace each with Henrikh Mkhitaryan and Marco Reus also on target for Jurgen Klopp's men.
Hamburg fought their way back into the game, making it 2-2 with goals from Zhi Gin Lam and Heiko Westermann, before capitulating under the force of a Dortmund side who have now won their first five games of the season.
Once Mandzukic made the breakthrough in the 51st minute the victory was never in any doubt, and Ribery duly made sure when he added a second after the hour mark.
Ivica Olic's goal was a scant consolation for the Wolves, who lost Luiz Gustavo to two cautions.
Schalke's second straight win was sealed by the Ghana international's strike in only his second game since joining from AC Milan.
Frankfurt dominated from start to finish against a Bremen side who spent much of the game with 10 men after Franco Di Santo saw red.
They were already behind at that point with Vaclav Kadlec scoring the first of his two goals before Aaron Hunt missed a penalty for the hosts, and an own goal from Sebastian Prodl summed up their day.
Halil Altintop and Tobias Werner supplied the goals for Markus Weinzierl's men, who came from behind to clinch a 2-1 victory after Admir Mehmedi gave Freiburg the lead.