The France Under-21 international replaced Danny Welbeck - absent with a knee problem - as the spearhead of Arsenal's attack and opened his account for the club in the second minute of this Group D clash at the Emirates Stadium on Wednesday.
A fine second-half strike from Alexis Sanchez - his 13th goal of an impressive season - sealed victory for Arsene Wenger's men, who came in for criticism after a 2-1 defeat to Manchester United in the Premier League on Saturday.
Arsenal needed just a point to be assured of qualification, but victory leaves them with a chance of sealing top spot in the group and avoiding a potentially tricky last-16 tie.
For Dortmund - already well off the pace behind leaders Bayern Munich in the Bundesliga - defeat ended their perfect record in the competition this season as a side missing influential playmaker Marco Reus through injury struggled to make much of an impact.
Both teams have seen their ranks depleted by injuries this season, and there was further concern for the hosts as first captain Mikel Arteta and then Sanogo were forced off during the second period.
That did little to disrupt their performance, however, as Wenger's men comfortably held on for their first win and clean sheet in four matches.
They were given an ideal start when Sanogo put them in front with the first action of note in the second minute.
The striker exchanged passes with Santi Cazorla - who came in following an ankle problem for Jack Wilshere - and, despite looking to be offside when the final ball was played, the Frenchman slotted a low finish through the legs of Roman Weidenfeller.
Arsenal goalkeeper Emiliano Martinez, in the side due to Wojciech Szczesny's hip injury, produced a fine sprawling save to deny Henrik Mkhitaryan as Dortmund continued to carry a threat with half-time approaching.
Alexis, who had been relatively quiet in the first period, brought a smart save out of Weidenfeller early in the second half with a stinging low drive from just outside the area.
