The Royal Blues had the upper hand in the first half but could not make their advantage count against the lethargic visitors.
Five minutes after the restart, however, Yevhen Konoplyanka was left unmarked in the box and drilled in to give Schalke the lead following a defensive mistake from Marcel Schmelzer.
Brazilian Naldo made sure of the points for Domenico Tedesco's team with a free-kick missile from 25 metres out in the 82nd minute.
To make matters worse for Dortmund, their forward Michy Batshuayi had to be taken off on a stretcher with an injury in stoppage time. The 24-year-old Belgian is on loan from Chelsea until the end of the season.
Schalke are second on 55 points with Dortmund dropping to fourth on 51, behind third-placed Bayer Leverkusen on goal difference, after they beat Eintracht Frankfurt 4-1 on Saturday.The top four teams qualify for the Champions League group stage.
Already-champions Bayern Munich crushed Borussia Moenchengladbach 5-1 on Saturday.
RB Leipzig came from a goal down but managed only a 1-1 draw at Werder Bremen to suffer a setback in their own Champions League aspirations.
Leipzig moved up to fifth on 47 but are still four points behind Dortmund.
(Reporting by Karolos Grohmann; Editing by Toby Davis and Clare Fallon)
