The victory took Dortmund on to 13 points and meant they won the group thanks to a better head-to-head record against the Spaniards, who drew 0-0 at Club Bruges.
Raphael Guerreiro got both goals for the Germans, the first when he tapped in following a fine counter-attack with a quarter of an hour gone and the second two minutes from time when he curled a shot into the top corner from around 10 metres out.
It was another fine performance by Dortmund, who even without several of their rested regulars extended their season's record to 17 wins, four draws and just one defeat in all competitions.
Monaco, who were destined to finish bottom of the group even before the game, suffered their 14th European match without a win and ended the group in last place with just one point, five points behind Bruges.
(Reporting by Andrew Downie; Editing by Ian Chadband)
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