Jurgen Klopp's men have bounced back from falling to the foot of the German top-flight standings, most recently beating Stuttgart 3-2 on the road.
Aubameyang and Gundogan scored either side of a Florian Klein penalty for Stuttgart, before Marco Reus all but sealed the three points for Dortmund late on.
Georg Niedermeier pulled one back for the home side, but it proved in vain as Dortmund continued their climb up the table.
Midfielder Gundogan said conceding multiple goals in their past two games was cause for concern.
"We've got to be somewhat self critical today despite the win," Gundogan said, as reported by Bundesliga's official website.
"We're getting ourselves in front in games, but haven't necessarily been able to keep countering the way we like to and then we end up conceding sloppy goals, like we did tonight from a late corner, which we should never allow to happen."
Gabon international Aubameyang said he was upbeat given his personal output - four goals in three games - but stressed their leaky defence must be addressed before their UEFA Champions League last-16 tie against Juventus, starting Tuesday.
"I've got the backing from the coach [Klopp] and being shifted into the central striker position is opening up more chances for me to find the net," the former Saint-Etienne man said.
"We're fine when it comes to scoring goals right now, but we have to maintain our concentration at the back against Juventus.
"Today we slacked off a little and can't afford that to happen on Tuesday. We're on the right track at present and we've just got to keep pushing forward."
Stuttgart have suffered due to Dortmund's recent rise, falling to last spot.
Earlier in February, Dortmund players Roman Weidenfeller and Mats Hummels reasoned with their fans following a defeat at home to Augsburg - but it was Stuttgart's turn to plea with their supporters on Friday.
"We went to talk to the fans after the game because we needed to demonstrate that we care and know that they're the most important part of this club," goal-scorer Klein said.
"Obviously we know it's difficult against Dortmund, you don't have a lot of time on the ball and it's a shame that after I equalised from the spot we weren't able to hold on until half-time.
"We made too many mistakes and you can't win games against teams like this if you do that. We have to stay positive."
