Stephen Stirling's spectacular strike was all that separated the sides after an even 90 minutes in which neither team played much in the way of sparkling football.
After netting five goals in three starts, Archie Campbell looked determined to maintain his scoring streak and saw a header acrobatically tipped onto the bar by David McGurn in the early stages.
Ex-Ton man Brian Graham created an opening for Rovers in the 25th minute when he charged clear down the right and rolled back for David Smith, who dragged wide with the goal at his mercy.
Clear-cut chances were at a premium, however, and besides a Graham drive straight at Derek Gaston after picking Craig Reid's pocket on the bye-line, defences were well on top.
It was going to take something special from either side to pick up the three points - and Stirling provided it in the 67th minute.
Chesting the ball down 25 yards out after Gaston's initial punt had been repelled by the Rovers defence, he lashed a swerving drive past McGurn to break the deadlock.
Despite a late barrage of long balls aimed at Simon Mensing, who had been pushed up front in a desperate attempt to salvage a draw, a Mark McLaughlin inspired Ton held out to record their third consecutive victory.
Morton boss Allan Moore said: "It was a bit scrappy and there weren't many efforts on target from either team. The game could've gone either way, but fortunately it went our way."
Morton (4-4-2): Gaston; Taggart, Reid, McLaughlin ©, Dyer; Stirling, Bachirou, Tidser, Graham; Weatherson, Campbell (Gormley [Trialist], 79).
Subs not used: Wallace, O'Ware, McDaid, Hutton (gk).
Booked: Taggart (29), Dyer (85), Stirling (90+1).
Raith Rovers (4-4-2): McGurn; Thomson, Mensing, Hill, Malone; Smith, Walker ©, S. Anderson, Hamill (G. Anderson, 78) ; Spence, Graham.
Subs not used: Ellis, Donaldson, Callachan, Laidlaw (gk).
Booked: Graham (1), Mensing (81), Hill (89).
Referee: George Salmond