A dominant start from Dortmund was rewarded on nine minutes, Marco Reus tapping into an empty net after Aubameyang had rounded the goalkeeper, before the Gabon international slotted home himself just after half-time.
The ever-threatening Aubameyang popped up again 18 minutes from time to finish off a superb team move on a comfortable afternoon for the visitors.
Victory eases the pressure on coach Jurgen Klopp, who earlier in the week dismissed talk of stepping down following a rotten run that had left the 2013 UEFA Champions League finalists propping up the division.
A first win in six Bundesliga games sees Dortmund leapfrog Freiburg into 16th, adding to the relegation worries of Christian Streich's men, who are now level on points with bottom-of-the table Stuttgart.
Few would have expected Freiburg to have a two-point lead over Klopp's men heading into the game, but there was little sign of the hosts adding to the woes of their opponents as Dortmund made much of the early pressing.
First Reus fired over inside two minutes, before Roman Burki was forced to parry away Shinji Kagawa's stinging shot four minutes later.
The hosts soon buckled under the pressure, contributing to their own downfall on nine minutes.
A poor back pass from Mike Frantz was seized upon by Aubameyang, who rounded the keeper to tee up Reus for a simple finish.
The lead allowed Dortmund, who made three changes from Wednesday's defeat to Augsburg, to take their foot off the gas as the half wore on, but they remained dominant.
Ilkay Gundogan curled a speculative effort just wide on 25 minutes, while only a poor connection prevented Kagawa from doubling the lead seven minutes later after some good work from the lively Aubameyang.
At the other end, Frantz fired wide after being set up by Mats Moller Daehli inside the area six minutes before the break, while visiting goalkeeper Roman Weidenfeller had to be alert to keep out Oliver Sorg's 25-yard half-volley.
Reus and Aubameyang continued to link up well after the interval, the former dinking a volleyed cross from the left to set up his team-mate, who fired wide from a central position.
Aubameyang was able to find the net after 56 minutes when he latched on to a sublime throughball from Gundogan to get behind the defence and slot home.
Dortmund refused to rest, with Burki on hand to palm away Reus' angled effort 10 minutes later, and the visitors added a third on 72 minutes.
A wonderful team move involving Reus, substitute Jakub Blaszczykowski and Kagawa allowed Aubameyang to pick his spot and make sure of a first win in 2015.
