Kagawa, who looks to have rediscovered his form this season, charged through in the 27th minute and sailed a perfect cross to the far post for Mats Hummels to head in.
Kagawa then chipped a brilliant pass for Matthias Ginter, whose cutback in the box found Pierre-Emerick Aubameyang and the Gabon international had no trouble netting his third goal in three games this season.
The 26-year-old crowd favourite had won two Bundesliga titles in 2011 and 2012 with Dortmund before joining Manchester United for a hapless two-year spell and returned last year.
Kagawa had the chance to score one himself in the 73rd but his 20-metre drive sailed narrowly wide with keeper Thomas Kraft out of position.
Hertha cut the deficit with substitute Salomon Kalou, who looked to be offside, tapping in on the rebound after a save from keeper Roman Buerki but Adrian Ramos scored in stoppage time to make sure Dortmund went top on goal difference.
“Obviously we struggled a bit as it was a bit hot today and we also paid the price for our many games recently,” Dortmund coach Thomas Tuchel told reporters, with his team having also qualified for the Europa League group stage in midweek.
“It is always better to be alone at the top rather than share it (with Bayern) but this is just a momentary snapshot. But it is a good ending ahead of the break for international matches,” he said.
Bayern, who beat Bayer Leverkusen 3-0 on Saturday to climb to nine points as well, are second, with VfL Wolfsburg third on seven after easing past Schalke 04 3-0 on Friday.
Borussia Moenchengladbach, third last season and preparing for their maiden Champions League group stage appearance, lost their third straight match, 2-1 at Werder Bremen, and are still looking for their third points of the season.
Werder, who took the lead with an Aron Johannsson spot kick before Lars Stindl levelled, grabbed the winner with Jannik Vestergaard’s glancing header eight minutes after the restart, climbing to four points with their first win of the campaign.
Gladbach also had Granit Xhaka sent off late in the game with a second booking.
(Reporting by Karolos Grohmann, editing by Mitch Phillips)