United boss Jim Goodwin had handed Ross Docherty his first start of the season, the captain replacing Kevin Holt in midfield - as he did before half-time in Sunday's league defeat by Rangers.
Goodwin cited the former Partick Thistle 31-year-old's composure on the ball for that switch and it paid off early as United looked the more creative force.
However, there was a lack of threat up front, while David Babunski and Kristijan Trapanovski, the summer signings who have impressed so far this season, failed to live up to the occasion before both were withdrawn.
The changes hauled United back into the game, with on-loan Wrexham striker Dalby looking dangerous before chesting down for Moult's equaliser.
However, the visitors had left it too late to come to life and, after that late sucker punch, will look back on this as an opportunity missed to reach their first semi-final since losing to Celtic in the 2015 final.