Captain Brown had been rested for Thursday's Europa League match against Dinamo Zagreb, but returned to notch two first-half goals at Celtic Park on Sunday.
Brown scored either side of James Forrest's strike, before Anthony Stokes added a fourth after the break to extend the leaders' winning run to eight straight league matches.
Sean Kelly had earlier cancelled out Brown's opener inside the first 10 minutes, as St Mirren started well, but their wretched sequence continues.
It was Gary Teale's first match in caretaker charge, following the sacking of Tommy Craig.
However, the player-coach could not prevent a fifth consecutive league defeat, which leaves St Mirren a point adrift at the foot of the table.
The victory gives Ronny Deila's side a comfortable cushion ahead of second-placed Inverness Caledonian Thistle, following their 4-0 defeat at home to Partick Thistle on Saturday.
