Cameroon-born Moukoko, who made his European debut as a 58th-minute substitute in Russia, broke the previous record of Celestine Babayaro, who was 16 years and 87 days when he played for Anderlecht in November 1994.
Dortmund, which had already qualified for the last 16, equalised within minutes of Moukoko's introduction, with Lukasz Piszczek cancelling out Sebastian Driussi's first-half goal.
Axel Witsel's low shot from the edge of the area on 78 minutes won the game for Dortmund as they secured top spot ahead of Lazio in Group F.
"It was an ugly win that was more about our mentality than our quality, but you have to win games like this too," Dortmund captain Marco Reus said.
"With all the injuries on top of that too, a win like tonight and finishing top of the group feels good."
Moukoko, who has already played for Germany Under-20s, broke a record for the second time in three weeks, having become the Bundesliga's youngest player on 22 November (AEDT), the day after his 16th birthday.
He has been promoted to Dortmund's senior squad after smashing scoring records in German youth football, having initially moved to Hamburg, his father's home city, from Cameroon in 2014.