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Bayern Munich took control of the title race with a thumping 5-0 win over Lucien Favre's side last weekend, but Dortmund returned to winning ways to leapfrog Niko Kovac's men ahead of their game with Fortuna Dusseldorf on Sunday.
England international Sancho was in scintillating form from the outset, scoring twice from close range inside the opening 24 minutes.
Mainz responded well to those early setbacks, twice hitting the post through Karim Onisiwo. Dortmund held on, though, to crank up the pressure on Bayern.
Jacob Bruun Larsen was denied early on by a smart stop from Florian Muller before Sancho scored his first, the 19-year-old steering home Mario Gotze's cross with a controlled half-volley from eight yards.
He then took his league tally for the season to 10 seven minutes later when his low effort from Thomas Delaney's cross crashed off Moussa Niakhaté and past the helpless Muller.
