McInally, a key member of United's UEFA Cup final team, saw his side take three points back north thanks to Steven Boyd's well-taken second-half goal.
United could have no complaints as Peterhead seized the initiative after a quiet first half.
Chances were at a premium in the opening period, with Ben Armour heading wide at the back post for the visitors.
Cammy Smith saw his flick blocked at the other end and Ian Harkes curled wide, while former Dundee midfielder Ryan Conroy came close for the visiting side.
Peterhead stepped up a gear after the restart and Scott Brown and Alan Cook threatened before former Hamilton forward Boyd produced a neat curling finish from Andrew McCarthy's cross.
United had a great chance to level but Smith could not connect from Paul McMullan's cross.
Harkes headed wide but Peterhead had a good opportunity to double their lead when the unmarked Cook shot straight at Deniz Mehmet from eight yards.
Visiting substitute Gary McKenzie managed to get booked for time-wasting while warming up, after kicking an extra ball on to the pitch.
United had some late aerial pressure but Ryan Edwards, Peter Pawlett and Louis Appere could not trouble Josh Rae in the visiting goal with headed opportunities.