The Paisley side dominated for large spells of a game played in heavy fog for the entirety of the second half but could not find the breakthrough.
United struggled to get into the contest but the point extended their unbeaten sequence in the league to four matches.
This was second-bottom St Mirren's first Premiership game for five weeks after a number of Covid-19-enforced postponements, with boss Jim Goodwin handing debuts to recent arrivals Brandon Mason and Jake Doyle-Hayes.
United in turn were unchanged from the side that had defeated Ross County at Tannadice the previous weekend.
The match took place at the newly-christened SMISA Stadium, renamed earlier in the day in recognition of the club's transition towards fan ownership next summer.
Heavy fog started to descend at the start of the second half but both teams continued to press for an opener. And from a Dennis lay-off, Mason's driven effort arced just over the crossbar.
The full-back then picked up the first booking of the game for a late tackle on Luke Bolton, before Jamie McGrath shot wide in another St Mirren chance.
The home side then had another chance from a dead ball but MacPherson's free-kick struck the wall and was cleared to safety, before Marcus Fraser shot just wide of goal as St Mirren pushed for the breakthrough.