Tobias Werner gave Augsburg the lead early on, but Jonathan Schmid and Admir Mehmedi turned things around to put Christian Streich's men on course for a much-needed win.
They failed to go the distance, though, with Paul Verhaegh, Halil Altintop and Andre Hahn all scoring inside the last 12 minutes to earn Augsburg all three points and take them to within a point of the top six.
Mehmedi lobbed the ball over the crossbar in the seventh minute as Freiburg went close early on.
Rather than celebrating taking the lead, they instead found themselves picking the ball out of their own net as Augsburg ran up the other end of the field with Altintop sending the ball over for Hahn, who headed the ball over the top for Werner to burst through and beat Oliver Baumann.
The lead lasted just 10 minutes before Schmid curled in a fine direct free-kick to level matters and give the hosts belief.
Indeed, Freiburg ended the half stronger and probably should have taken the lead before the interval with Mehmedi and Schmid both wasting good opportunities.
The heavy rain added an extra challenge for both sides in the second half with the quality of play deteriorating with chances reduced to a minimum at both ends.
Freiburg finally found a way out of the midfield monotony to take the lead in the 73rd minute with Mehmedi using the slick surface to his advantage with a low shot which flashed past Alexander Manninger, gathering pace as it skidded in.
Augsburg managed a scrappy equaliser five minutes later with a deflected cross reaching Verhaegh, who found the corner of Baumann's goal with his shot, silencing the home fans.
It was a cruel blow to the hosts, who were unable to recover from it either as Augsburg sensed their chance to turn one point into three, taking it with Altintop scoring one of the easiest goals of his career to make it 3-2 in the 84th minute.
Hahn then completed the victory in stoppage time, beating Baumann with a left-foot shot which took Augsburg to within a point of the top six and increasing their chances of playing in Europe next season.