The striker scored after 4, 61 and 85 minutes to inspire Dortmund to win 4-0 on the night – and 4-1 on aggregate.
He made amends for spurning a host of chances in Lisbon, including a missed penalty.
“After the first leg, I was very sad and really unsatisfied with my performance,” the 27-year-old the official club website.
“I made a lot of mistakes throughout that match. So I wanted to show my team-mates today that I’m capable of much more.
“I’m very happy that we won and that we made it through. Tonight was absolutely fantastic.”
After Dortmund reached the Champions League quarter-finals for the first time since 2014, coach Thomas Tuchel joked about Aubameyang’s performance in the first leg.
“After we had fielded Aubameyang’s twin in Lisbon, we were happy to have him back for tonight’s game,” he told reporters.
The striker now has seven goals from seven games in this season’s competition.
The hat-trick could hardly have come at a better time after Aubameyang irritated club officials on Saturday when sporting a Nike ‘swoosh’ logo in his hair during the 6-2 victory over Bayer Leverkusen.
The athletics brand’s rival Puma is a shareholder in Dortmund, so prompting club officials to say they would be talking to the 2015 African Footballer of the Year about the matter.
One of those was sporting director Michael Zorc, who adopted a different tone when talking about Aubameyang’s heroics at the Westfalenstadion on Wednesday.
“I said to ‘Auba’ after the first leg: ‘You’ll decide the second leg’ – and that’s exactly what happened,” Zorc beamed.