A new and distinct Torenia plant named 'Dantopinkmn' particularly characterized by having shiny green foliage, doted with plenty of delicate, funnel form, cup shaped flowers in shades of pale and dark purple; bush, cascading, rounded and compact growth habit and densely branched; vigorous growth; early flowering, flowers all year round in moderate climate; suitable for use as an annual for hanging pots outdoors under partial shade; and good weather tolerance with preferred temperature range of 15-25 C.