Michael Tidser scored the only goal of the game as Morton edged past Raith 1-0.
Chances were at a premium in a poor first half, with Allan Walker having the first shot on target for the visitors moments before the break but he couldn't find a way past goalkeeper Derek Gaston.
They went closer seconds later as Gaston was forced to tip Brian Graham's effort round the post to ensure they went in level at the break.
But it was the hosts who broke the deadlock eight minutes after the restart when Tidser produced a fine strike from the edge of the area.
Substitute Colin McMenamin went close to a second but his close-range header was smartly kept out by David McGurn.
Rovers twice went close through Graham and Patrick Clarke in the latter stages but couldn't find the breakthrough.