Andy Murdoch’s late goal was enough to move Morton back into the top half of the table and leave Brechin still searching for their first win.
Bob McHugh and Connor McLennan traded early efforts without troubling either keeper as the sides battled for the initiative, but genuine opportunities were at a premium.
The visitors, though, stepped up a gear as the interval approached and Ross Forbes drilled a free-kick just over before Murdoch was also off target with another long range shot.
Morton should have broken the deadlock on the restart but Thomas O’Ware somehow sent his header wide from a few yards out.
Brechin boss Darren Dods and his Morton counterpart Jim Duffy made a series of substitutions in a bid to find the missing spark and it almost had the desired effect for Duffy when Gary Harkins tried a 14-yard shot which forced Graeme Smith’s first save.
But Smith was beaten six minutes later when Murdoch picked up a loose ball on the edge of the box and drilled his shot low.