Otto Rehhagel, who will take over as manager of Hertha tomorrow [Sunday], followed the game from his home in Essen as his new side suffered their sixth straight defeat.
In truth Hertha had enough chances to win the game, but Grosskreutz's strike proved the difference and saw Bayern lose ground as they drew 0-0 at Freiburg.
Dortmund's closest challengers are now Borussia Monchengladbach, who moved second, a point ahead of Bayern, with a 2-1 win at Kaiserslautern.
Two goals in five first-half minutes from Patrick Hermann and Juan Arango put Gladbach in the driving seat, but a stunning strike from Leon Jessen gave Lucien Favre's side something to worry about in the second half.
Bayer Leverkusen bounced back from their midweek Champions League disappointment with a 4-1 win over Augsburg.
Stefan Kiessling was on target twice as Robin Dutt's side took all three points four days after losing at home to Barcelona.
Gonzalo Castro and Andre Schurrle were also on the scoresheet, with Koo Ja Cheol's 50th-minute briefly having given Augsburg hope.
Werder Bremen saw off Hamburg 3-1 in their northern Germany derby.
Marko Marin, Tom Trybull and Marko Arnautovic scored the goals for Thomas Schaaf's side, with Mladen Petric pulling one back for the hosts.
Tomas Pekhart grabbed the winner as Nurnberg claimed a 2-1 win over Cologne at the Frankenstadion.
Alexander Esswein gave Dieter Hecking's side the lead in the 28th minute and Milivoje Novakovic brought Cologne level in the 66th minute, before Pekhart's intervention five minutes from time.