Matias Vecino made it 4-0 and Dzeko’s late double put the gloss on his side’s display before Arthur Theate struck a late consolation.
Riccardo Saponara came off the bench to inspire Fiorentina to their third straight win with a 2-1 success at Genoa.
The Viola had their chances in the first half but it took a stunning strike from Saponara after cutting in from the left flank in the 60th minute to break the deadlock.
Saponara then set up his side’s second for Giacomo Bonaventura before Domenico Criscito scored a penalty with the last kick of the game.
Ten-man Atletico Madrid edged back to the top of LaLiga but were fortunate to cling on for a goalless draw against unbeaten Athletic Bilbao.
The hosts had substitute Joao Felix sent off in the 78th minute for dissent, after he protested his initial booking for a foul on Bilbao’s Unai Vencedor.
And Diego Simeone’s men almost lost the game in injury time when Asier Villalibre missed a golden chance for the visitors.
An early Oscar Trejo penalty paved the way for Rayo Vallecano to ease past still-pointless Getafe 3-0, with late goals from Pathe Ciss and Radamel Falcao confirming the home side’s victory.
Elche and Levante shared a 1-1 draw, with Jose Luis Morales netting for the visitors to cancel out a 33rd-minute opener from Lucas Perez.
And there was no let-up for the struggling visitors after the interval as Robert Lewandowski fired home on the hour-mark, scoring in a 19th successive Bayern appearance, followed by a second for Kimmich before Eric Maxim Choupo-Moting rounded off the rout.
RB Leipzig avoided a third straight defeat but their sluggish start to the new season continued as they were held to a 1-1 draw at Cologne.
Anthony Modeste scored a 53rd-minute opener for the home side but Amadou Haidara’s powerful 71st-minute header ensured Leipzig a fourth point from five matches.
Florian Neiderlechner came off the bench to secure Augsburg’s first win of the season with a 1-0 triumph over Borussia Monchengladbach, while the games between Mainz and Freiburg, and Arminia Bielefeld and Hoffenheim, ended goalless.
In a match marred by an outbreak of crowd trouble at half-time, Frankowski struck a 71st-minute winner to send his side into second place and leave Lille languishing on just five points from their first six games.