The Buddies controlled the early exchanges and were rewarded when Kenny McLean opened the scoring with a well struck free-kick just after the half-hour mark.
Jon Robertson added a second with a wonderful volley four minutes before half-time.
The second half followed a similar pattern to the first 45 minutes, however the home side found Brechin keeper Craig Nelson in inspired form and were unable to add to the scoring.
A slow start to the match brought little in the way of goalmouth action and John McGinn's wild shot over the bar was the home team's only attempt during the opening 10 minutes.
Kenny McLean failed to find the effort from distance after 15 minutes before Nelson did well to parry Marc McAusland's powerful shot past the post.
Nelson held McLean's strike from the edge of the box as the hosts started to increase the pressure on the Brechin goal.
Gary Teale ended a direct run with a shot that rattled the outside of the post, much to the frustration of Lewis Guy who was well placed inside the area.
The opening goal finally arrived after 31 minutes when McLean's well struck free-kick found the bottom right-hand corner of Nelson's goal.
Following the goal Danny Lennon was forced into a first-half substitution, when McGinn limped off to be replaced by Dougie Imrie.
Ray McKinnon made a change of his own with nine minutes remaining in the first-half - the injured Jonathan Brown making way for Jonathan Stewart.
St Mirren doubled their lead four minutes before the break when Robertson brilliantly volleyed home from Teale's corner.
Nelson did well to tip over from McLean before the visitors passed up a good opportunity to reduce the deficit - Derek Carcary was denied by the feet of the Samson before failing to hit the target with the rebound.
Guy came agonisingly close to putting the game beyond City when he met Davin van Zanten's perfect cross at the back-post, however was denied as the ball looped over Nelson and struck the bar.
Guy turned provider for St Mirren's next chance, knocking the ball down for Sam Parkin who forced Nelson into a fantastic stop from point-blank range.
There were further chances for Thomas Reilly and Teale in the final minutes of the match, but Saints were unable to increase their lead further.