Before kick-off, Dortmund coach Peter Stoeger revealed he took a dim view of Aubameyang missing a team meeting on Saturday and threw the top-scorer out of the squad.
Dortmund's attack struggled to finish in his absence, testing visiting goalkeeper Koen Casteel's with only one of 19 attempts on goal.
"There are rules which apply to every player, regardless of how many goals they score, and it was a logical step," said Dortmund keeper Roman Burki.
"We missed his goals today, that was obvious, and we hope that we won't be without him again for more games after another dumb mistake."
It is the third time Aubameyang has been disciplined by the club after an unauthorised video shoot at Dortmund's training ground last November and a trip to Milan shortly before a Champions League game last season.
In Aubameyang's absence, 18-year-old Swedish striker Alexander Isak made only his third Bundesliga appearance up front having previously played just 13 minutes in the top flight.
Isak clipped the post with a first-half shot while winger Andriy Yarmolenko howled in rage after firing wide.
Dortmund kept up the pressure after the break when England Under-19 star Jadon Sancho, 17, -- who also made only his third appearance in the Bundesliga -- hit the post early in the second half.
At the other end, Daniel Didavi fired at Burki in the first half while new signing Renato Steffen, recruited from Basel, was also denied after coming on with 25 minutes left.
The result leaves Dortmund in the fourth and final Champions League spot, but only one point clear of Bayer Leverkusen and Borussia Moenchengladbach, who had earlier fallen to a shock 2-1 defeat at bottom club Cologne.
New signing Simon Terodde hit a 95th-minute winner as Cologne made it two victories in a row, having gone winless for their first 16 games of the campaign.
Cologne remain eight points from safety even after Terrode, who was making his club debut after signing from Stuttgart in December, reacted quickest in the box by firing home a loose ball with time almost up.
The victory comes after the club's new CEO Armin Veh told German daily Bild "no one believes that we'll manage it", in terms of Cologne's survival chances.
Danish defender Frederik Sorensen gave Cologne the lead against the run of play when he headed home a free-kick by Serbia midfielder Milos Jojic on 34 minutes.
Cologne goalkeeper Timo Horn somehow managed to keep Gladbach's attack at bay as the visitors attacked in waves, with Germany midfielder Christoph Kramer and Belgian forward Thorgan Hazard both going close.
The pressure paid off when the visitors drew level as Raffael pounced on a Horn save and fired home off the underside of the crossbar in the 69th minute, only for Terrode to strike with his last-gasp effort.
On Saturday, RB Leipzig climbed to second in the table with a 3-1 win over Schalke after Liverpool-bound Naby Keita scored their opening goal.
The Guinea midfielder has a contract to join Liverpool next season, but on Sunday Leipzig put out a statement insisting he will not be moving to Anfield this month, despite speculation he could make an early departure.
Bundesliga leaders Bayern Munich are 13 points clear in the table after their 3-1 win at Bayer Leverkusen on Friday, with Franck Ribery, James Rodriguez and Javi Martinez scoring the goals.
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