Stoeger took over from sacked Peter Bosz on Sunday and the Austrian celebrated a winning start that will ease the pressure on the Ruhr valley club.
Centre back Sokratis Papastathopoulos fired in on the rebound after the ball bounced off the post in the 55th minute and Japan international Shinji Kagawa slotted in from a Pierre-Emerick Aubameyang assist in the 89th to make sure of the points.
The victory ended Dortmund's disappointing run of eight consecutive Bundesliga matches without a win and lifted them back up the table into fourth on 25 points.
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Borussia Moenchengladbach slumped to a 1-0 loss at strugglers Freiburg to drop down to sixth on 25, level on points with Eintracht Frankfurt, who moved up to fifth after beating hosts Hamburg SV 2-1.
Bayern, top on 35 points, host bottom club Cologne on Wednesday.
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