The Colombia striker, who had been out of action for four weeks with a hip injury, struck in the second half to lift the principality team on to 74 points from 31 games.
They lead Nice by four points and champions Paris St Germain, who host En Avant Guingamp on Sunday, by six.
Monaco, who lost 4-1 to PSG in the League Cup final last Saturday, travel to Dortmund on Tuesday.
Falcao's return allowed coach Leonardo Jardim to rest French prodigy Kylian Mbappe, as well as influential midfielder Thomas Lemar.
Read the full article on eurosport.co.uk: Falcao back to help Monaco beat Angers