The German side made it 21 goals across their six matches during their 2-2 draw with Real Madrid on Wednesday.
This meant they beat the previous best of 20 set by Real Madrid in 2013-14, Barcelona in 2011-12 and 2016/17 and Manchester United in 1998-99.
Marco Reus scored the crucial goal with only two minutes of normal time to play, with Pierre-Emerick Aubameyang having earlier got on the scoresheet as Dortmund came from two goals down to force a draw.
The result means that the Bundesliga side finish top of Group F on 14 points, two ahead of holders Madrid.
The majority of Dortmund's goals came against Legia Warsaw, who they scored 14 against in total.
Sporting Lisbon were the only side to limit Thomas Tuchel's men to scoring just one goal in a match.