Manuel Akanji, Erling Haaland, and Mats Hummels all scored during a 23-minute window to claim the victory for Dortmund, extending Schalke's winless run in the league to 21 matches dating back to January.
Schalke did well to resist Dortmund's advances in the first half before Akanji opened the scoring 10 minutes after the interval. The Swiss defender pounced on the rebound from Frederik Ronnow's initial save on a Raphael Guerreiro effort following a slick bit of interplay from the corner kick.
Haaland doubled the hosts' advantage with his 23rd goal in 26 competitive outings for Dortmund six minutes later when the Norwegian got on the end of Jadon Sancho's perfectly weighted pass, blasting it past Ronnow at the near post.
Haaland has now netted 18 goals in his first 20 Bundesliga matches, which is second-best all-time behind only Uwe Seeler, who recorded 19 in 20 with Hamburg in 1963-64.
Hummels iced the result with a header 12 minutes from time. The German central defender improved his record to 12 unbeaten against Schalke with Dortmund and Bayern Munich.
Schalke didn't manage a shot on target over the 90 minutes, and they were outshot 18-3 while finishing with only 25% possession.
Die Knappen remain second from bottom on one point after compiling four defeats in five matches and a minus-17 goal difference. The victory moves Dortmund to joint-second in the table alongside Bayern Munich, one point adrift of league leaders RB Leipzig.