By Mark Buckingham
Last Updated: 01/01/70 1:00am
The champions were in scintillating form on home soil and opened the scoring through Dutch international striker Roy Makaay on 22 minutes.
Inspirational midfielder Michael Ballack doubled the advantage on the stroke of half time before Bastian Schweinsteiger made it three before the hour mark.
Niko Kovac notched a consolation on 65 minutes but Hasan Salihamidzic rubbed salt into the wounds on 88 minutes, leaving Stevens's future as Hertha coach dangling by a thread after a winless start to the Bundesliga season.
Stuttgart preserved their record of not conceding a Bundesliga goal this season but they were unable to make the breakthrough as Cologne garnered a commendable point on the road.
Borussia Dortmund continue to keep pace with the leaders after Giuseppe Reina's 11th minute goal secured the three points at struggling Eintracht Frankfurt.
In the battle of the sides in the relegation zone, Hamburg came from behind to prevail against Borussia Monchengladbach.
Arie van Lent put the visitors ahead on 18 minutes but a second half brace from Sergei Barbarez handed a precious win to Hamburg.
Schalke breathed life into their season after overcoming an early goal to record a vital win at Hannover.
Thomas Christiansen scored for Hannover on 16 minutes but Gerald Asamoah and Dario Rodriguez gave Schalke the points before the break, with the hosts having Julian de Guzman dismissed after the interval.
VFL Bochum produced a stunning second half display to dispose of ten man Kaiserslautern after a torid opening period which saw the visitors have Marian Hristov sent off on the half hour for two yellow cards.
Vahid Hashemian broke the deadlock on 49 minutes before Peter Madsen extended the lead on the hour, and the same pairing netted again inside the last ten minutes to give Bochum a convincing 4-0 triumph.
Freiburg remain in the top half of the table after Zlatan Bajramovic's 77th minute goal sealed a slender success at home to 1860 Munich.