Germany international Grosskreutz scored from a tight angle after goalkeeper Thomas Kraft palmed away a Robert Lewandowski header to lift Dortmund to 49 points from 22 matches, three ahead of Borussia Monchengladbach who won 2-1 at Kaiserslautern.
Bayern Munich stumbled to a goalless draw at bottom club Freiburg to drop four points off the lead in third place.
Dortmund are now unbeaten in 16 league games while Hertha, who appointed Otto Rehhagel as coach ahead of their 1,000th Bundesliga game, remained 15th after slumping to a fifth straight league defeat.
"It does not always have to be beautiful football," Grosskreutz told reporters after Dortmund's sixth straight league win. "The main thing is we got all three points."
Dortmund, missing attacking midfielders Mario Gotze and Shinji Kagawa, lacked their usual creativity and apart from two efforts by Lucas Barrios had little to show for the first half in front of a sell-out 74,000 crowd at the Olympic Stadium.
Hertha took control after the break and Patrick Ebert twice fired narrowly wide in a four-minute spell.
Dortmund struck at just the right time, Grosskreutz's goal deflating Hertha hopes of a first league win since October.
Bayern did not look serious title contenders at Freiburg and not even the introduction of Dutch winger Arjen Robben in the second half could change their fortunes.
Goals from Patrick Herrmann and Juan Arango kept Gladbach, who needed to win a play-off last season to avoid relegation, flying high.
But Hermann, who has been in the running for a Germany call-up, faces several weeks on the sidelines after breaking his collarbone in a first-half collision with Kaiserslautern defender Florian Dick.
"It is a pity for him after the season he has had and it is a pity for us," said Gladbach coach Lucien Favre. "Let's hope he is back in six weeks."
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.
Bayer Leverkusen bounced back from their midweek defeat by Barcelona in the Champions League to crush second from bottom Augsburg 4-1, forward Stefan Kiessling netting twice.
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