Dortmund's Kevin Grosskreutz (Photo: AP)
Germany international Grosskreutz scored from a tight angle after keeper Thomas Kraft palmed away a Robert Lewandowski header to lift Dortmund to 49 points, three ahead of Borussia Moenchengladbach who won 2-1 at Kaiserslautern.
Dortmund are now unbeaten in 16 league games.
Bayern Munich, five points off the pace, visit Freiburg later on Saturday.
Hertha, who appointed Otto Rehhagel as coach ahead of their 1,000th Bundesliga game, remained 15th after slumping to a fifth straight league defeat.
In an entertaining northern derby, fifth-placed Werder Bremen won 3-1 at Hamburg SV with goals from Marko Marin, Tom Trybull and Marko Arnautovic.
Mladen Petric was on target for the hosts.
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