The win, which kept Dortmund in fourth place and on course for Champions League football next season, was set up by Sancho's first goal since returning from Manchester United on loan in January.
Sancho dribbled in from the left flank before scoring in a trademark solo effort reminiscent of his peak at Dortmund three years ago.
"Doing something like that, you can of course see what a great footballer he is," Dortmund sporting director Sebastian Kehl said of Sancho.
The goal put Dortmund 2-0 up, but the visitors lost Marcel Sabitzer to a straight red card shortly after and held on for a half to ensure a 2-1 win.
It was his first goal in eight matches after returning to the side - and his first in Dortmund colours in 1,031 days dating back to May 2021.
Kehl, who played a key role in bringing Sancho back to the club on a loan until the summer, said the 23-year-old was "rewarded" for his hard work.
"You can see how he can make the difference, especially in one-on-one situations."
Prior to Saturday, Sancho had laid on two assists since returning in January.
"Everyone is happy for Jadon because they saw how hard he was working and how willing he was to help the team.
"Goals help. He's had one or two assists before, but this goal will help him and give him a boost."
Sancho had barely played this season after falling out with United manager Erik ten Hag, who would not allow him to train with the first team.
Dortmund coach Edin Terzic, who was in charge as an interim manager when the Black and Yellows won the German Cup in 2021 thanks to two goals from Sancho, praised the winger.
"It's an example of what he's capable of and hopefully he can continue like this.
"He's not limiting himself to scoring a goal - it was his entire performance.
"We know he's not 100 per cent, there's no way he can be (after a long lay-off). But we'll get him there."
Kehl compared Sancho's return to a player returning from injury and said Dortmund would need the winger in Wednesday's Champions League last 16 second leg at home to PSV Eindhoven.
"You should not forget that he didn't play for a long time. It's like when a player has a cruciate ligament injury and is out for a long time.
"We need him and we will again on Wednesday and for the coming weeks."
Dortmund drew 1-1 in the first leg in the Netherlands and need a win to ensure progression to the quarter-finals.
