The Gabon international was dropped from their Champions League win against Sporting hours before the start of that game after he had made an unauthorised trip to Milan with friends on Monday.
The striker silently accepted the ban and sat in the stands before delivering his best scoring performance on Saturday as he gave Dortmund their first win since late September to move up to fifth place on 18 points.
"I realise I made a mistake and I wanted to apologise to my team mates and my coach," said a beaming Aubameyang, who has scored 11 times in the league and is joint top scorer with Cologne's Anthony Modeste.
The 27-year-old Aubameyang opened his account after four minutes with an easy tap-in and had completed his hat-trick by the 27th minute, helped by a string of Hamburg errors.
Aubameyang grabbed another three minutes after the restart with a low diagonal shot to complete his first four-goal haul in a Bundesliga match.
"It was very good. I feel very happy tonight," Aubameyang told reporters. "It was an important game for us after four matches without a win.
"It was a good reaction for the team and especially for me."
The forward will also be key for the Champions League after Dortmund's win over Sporting secured a spot in the knockout stage with two matches to spare with the striker scoring three goals in three games.
"Tonight we had no other alternative to winning," Dortmund coach Thomas Tuchel told reporters. "We wanted this result and that's exactly how we played. Auba's four goals are of course beyond all expectations.
"It was and still is clear that we cannot achieve our goals without Aubameyang," he said.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
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