Since returning to the club on an initial loan period from Real Madrid, Sahin had started only one game prior to Saturday's victory.
He made up for lost time with two goals and an assist, almost single-handedly downing Freiburg and making the critics eat their words.
"I owed this to the club," he said. "It was important for me for the penny to drop sooner or later and the coach always said it was just a matter of time.
"I had a good feeling. I knew I had to play well today because my son was in the stadium.
"It had to be a special game and I, or we, managed it."
Sahin thanked coach Jurgen Klopp for keeping faith in him after a difficult few months since arriving from Liverpool, where he had not been playing regularly.
"I played a few bad passes, but that's part of my game and you can get away with that with this coach," he told Sky television.
"That does you good. It's not only the coach, though. The whole club is standing behind me in the same way the coach is, and you only get that here.
"I owed something to them, and I owe them something still, but I think I contributed to us winning this game."