The 18-year-old, who has scored five goals and set up six in a sparkling season so far, started a quick move down the left and then deftly slotted home the winner in the 74th minute to give Dortmund their first win over Schalke since 2015.
England international Sancho had missed training earlier this week to return to England due to a death in the family.
"It was a very hard week for him," said Dortmund coach Lucien Favre. "Jadon returned from London only yesterday evening. But he really wanted to play."
Dortmund's Thomas Delaney had earlier silenced the 60,000 crowd with a glancing header in the seventh minute after Marco Reus whipped a free kick into the box.
Bundesliga leading scorer Paco Alcacer then came close with a powerful shot as the visitors confirmed their title favourites tag with a dominant opening period.
The Royal Blues' fate looked to have been sealed late in the first half when their last fit forward, Guido Burgstaller, who had their best chance on the half-hour, had to go off injured.
However last season's runners-up, already missing injured forwards Mark Uth, Franco di Santo and Breel Embolo, earned a surprise penalty to level through Daniel Caligiuri on the hour.
Sancho then completed another fine performance to secure a fifth straight league win that lifted undefeated Dortmund to 36 points, nine ahead of second-placed Bayern Munich, who beat Nuremberg 3-0. Schalke dropped to 13th on 14 points.
"Schalke were well organised and it was hard in the first half," said Favre, who is now unbeaten in his 14 league games in charge of Dortmund. "My team stuck with it after the penalty and that was crucial. We deserved the win today." (Reporting by Karolos Grohmann; Editing by Ken Ferris)
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