As the only teams in Germany's top flight to have won their opening three matches, Dortmund are matching Bayern's impressive early form as the Bavarians bid to become the first side to win fourth straight German titles.
Dortmund are top on goal difference from Bayern, who romped to a 3-0 home win over Bayer Leverkusen on Saturday.
Borussia saw off Hertha at their Westfalenstadion with goals from captain Mats Hummels, Pierre-Emerick Aubameyang and Adrian Ramos.
"The hardest thing today was to keep the pace up," said Hummels, who said his side were feeling the effects of Thursday's 7-2 win at home to Odds BK to qualify for the Europa League's group stages.
"It wasn't a good performance from us, but we still won.
"We could have decided it earlier and it was annoying to concede the late goal, because we were a little flat."
Pitchside temperatures of 32 degrees Celsius (89.6 Fahrenheit) meant frequent water breaks as Dortmund continued their red-hot form when Hummels powered home a Shinji Kagawa cross on 27 minutes.
Aubamenyang claimed his seventh goal in eight games after right-back Matthias Ginter combined with Kagawa to set up a simple tap-in on 51 minutes.
Ex-Chelsea striker Salomon Kalou pulled a goal back for Hertha on 78 minutes before Colombia striker Adrian Ramos came off the bench to score Borussia's third in injury time.
Champions League side Borussia Moenchengladbach are enduring their worst start to a Bundesliga season as three straight league defeats left them bottom after losing 2-1 at Werder Bremen.
Bremen's American striker Aron Johannsson netted a first-half penalty before Gladbach's Lars Stindl levelled just before the break, but towering Denmark defender Jannik Vestergaard headed the winner on 53 minutes.
Gladbach's Swiss midfielder Granit Xhaka was sent off for a second yellow card on 87 minutes, but Felix Kroos, brother of Real Madrid star Toni, fired the subsequent penalty wide.
Wolfsburg are third after beating Schalke 3-0 at home on Friday without attacking midfield star Kevin de Bruyne, who completed his transfer to Manchester City on Sunday.
On Saturday, Bayern downed Leverkusen as Thomas Mueller scored twice, to leave him with five goals in his opening three league matches, before new Netherlands captain Arjen Robben netted a late penalty.
Cologne finish the weekend fourth after a 2-1 comeback win at home to Hamburg in controversial fashion.
Lewis Holtby gave Hamburg a second-half lead before Cologne levelled through Philipp Hosiner on 76 minutes.
But the game turned on a dubious red card and penalty.
Hamburg's ex-Bosnia captain Emir Spahic was sent off on 79 minutes for the slightest of touches on Cologne striker Anthony Modeste, who drilled home the spot-kick to the fury of the visitors' bench.
Japan striker Yoshinori Muto warmed up for his country's World Cup qualifier against Cambodia in Saitama on Thursday with his first two Bundesliga goals in Mainz's 3-0 win over Hanover before Yunus Malli claimed their third.
Socceroos forward Mathew Leckie also scored his first goal in Germany's top flight in Ingolstadt's 1-0 win at Bavarian rivals Augsburg with a superb shot inside the left-hand post on 63 minutes.
Ten-man Stuttgart are second from bottom after a 4-1 defeat at home to Eintracht Frankfurt as Poland goalkeeper Przemyslaw Tyton was sent off for the hosts.
Darmstadt are 12th after their third straight draw following a goalless effort at home to Hoffenheim.