Dortmund rode their luck all evening to bag the three points that saw them move on to 46 from 25 games, three behind second-placed RB Leipzig and four ahead of Hoffenheim in fourth.
Leaders Bayern Munich, who are 10 points clear on 59, visit Borussia Moenchengladbach on Sunday. Leipzig travel to lowly Werder Bremen on Saturday.
Despite a lacklustre performance, Dortmund extended their unbeaten home run in the Bundesliga to 33 matches, with their last defeat dating back to April 4, 2015.
The hosts needed one moment of brilliance to win, with Gabon international Aubameyang slotting in beautifully with his left foot after a perfectly timed cutback from Marcel Schmelzer in the 14th minute for his 23rd league goal of the campaign.
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Dortmund, who face AS Monaco in the Champions League quarter-finals next month, lacked order at the back despite the return of central defender Sokratis Papastathopoulos.
They needed outstanding goalkeeping from Roman Buerki, especially in the first half when he denied Ingolstadt four times, including clearing off the line, to protect the lead.
Dortmund were even less aggressive after the break and failed to get a single shot on target, allowing Ingolstadt to reclaim the initiative.
But the struggling visitors, who are second-bottom on 19 points, seven from the safety zone, could not find an equaliser, with Marvin Matip curling a shot wide four minutes from time and Mathew Leckie firing over with the last kick of the game.
(Reporting by Karolos Grohmann; Editing by Ken Ferris)
