Sancho, 19, slipped the ball through for Achraf Hakimi to coolly finish in the 2nd half for Dortmund’s winner.
It means Sancho draws level with Henrikh Mkhitaryan’s record in a single season, with the Armenian placing up 15 goals all through the 2015-16 campaign.
Thorgan Hazard scored the opener with Lars Stindl levelling for the hosts.
Dortmund go up to second – one point at the back of league leaders Bayern Munich, who play Augsburg on Sunday.
Lucien Favre’s side took benefit of RB Leipzip’s goalless draw at Wolfsburg.
Dortmund face Paris St-Germain in the 2nd leg of the Champions League last-16 tie on Wednesday, going into the game with a 2-1 advantage.