Gabon forward Pierre-Emerick Aubameyang's goal early in the second half turned out to be decisive for Dortmund after Shinji Kagawa and Matthias Ginter gave them a 2-1 halftime lead. Dutchman Klaas-Jan Huntelaar scored both goals for Schalke.
Dortmund have scored in each of their 22 competitive games since coach Thomas Tuchel took over before the start of the season, amassing a total of 71 including 35 in the Bundesliga.
The win keeps Dortmund second in the Bundesliga with 29 points, five points behind unbeaten leaders Bayern Munich who defeated VfB Stuttgart 4-0 on Saturday to take their tally to 34 points out of a possible 36. Schalke are fifth on 20.
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Dortmund broke through in the 30th minute when Ginter got away from Dennis Aogo and sent over a pinpoint cross for Kagawa to head in.
Schalke did not take long to hit back as Leroy Sane set up Huntelaar for the equaliser three minutes later but Dortmund regained the lead two minutes before halftime when Ginter got on the end of Henrikh Mkhitaryan's corner.
The hosts struck again early in the second half after a counter-attack ended with Gonzalo Castro finding Aubameyang, who fired in from 14 metres.
Ilkay Gundogan and Mkhitaryan were both foiled by Schalke goalkeeper Raul Faehrmann as Dortmund threatened to run away with the points, but instead the hosts were forced to endure a nail-biting finale.
Huntelaar pulled one back after pouncing on a mistake by Dortmund captain Mats Hummels in the 72nd minute and substitute Pierre-Emile Hoejbjerg almost snatched a point when his effort struck the post.
(Writing by Brian Homewood in Berne, Editing by Ian Chadband)
