Having suffered a goalless draw against Union Berlin in the Bundesliga last time out, Dortmund were determined to get on the scoresheet early here.
Fabio Silva was a livewire, twice being denied by Stas Pokatilov, before Serhou Guirassy blasted over.
The latter then broke the deadlock inside just 10 minutes, tucking in the rebound after Pokatilov spilled Felix Nmecha’s initial strike.
Dortmund continued to threaten, and Pokatilov produced a fine double save to first stop Joey Veerman’s free-kick, then Carney Chukwuemeka’s rebound.
However, Sabah grew in confidence and thought they were level at the half-hour mark when Joy-Lance Mickels curled into the top corner, only for it to be disallowed for a marginal offside.
Nevertheless, the hosts eventually found an equaliser before half-time through Aden McCarthy, who scored his first goal for the club by heading home Tymoteusz Puchacz’s free-kick.
Kaheem Parris then forced a decent save from Gregor Kobel as momentum swung.
After the restart, though, Dortmund regained control, and it did not take long for them to get their noses in front again.
Veerman crossed towards the back post, where Guirassy was on hand to bury a side-foot volley - his fourth goal in the competition this term to already match his total from the previous campaign.
Despite going behind for a second time, Sabah did not seem too disheartened and kept driving forward, with Mickels next to test Kobel from range.
Both teams missed decent opportunities in the latter stages, as Silva failed to add to his four goals this season by striking wide when through on goal, before Sabah substitute Orphe Mbina shot off target from a similar position.
Ultimately, Dortmund held on for a narrow victory, just their third in seven Champions League matches (L4).
Sabah, meanwhile, lost their perfect home record in European fixtures this term (W5) and will aim to bounce back with their first away win at this level against Viking next time out.
Flashscore Man of the Match: Serhou Guirassy (Borussia Dortmund)
