After an early Brian Fairbairn cross was cleared, Morton began to probe at Raith's rearguard and Templeman shot well wide before Jim McAlister tested Michael Brown with a stinging drive.
Raith hit back and Ian Harty forced a save from David McGurn but the opening goal was unexpected as both sides were unable to make a decisive break. Steven Bonar was hopelessly short with a pass-back to Brown and Templeman remained composed as he intercepted and lobbed the ball over the stranded 'keeper.
Templeman had another astute lob tipped over by Brown and had his header from the resultant corner-kick saved by the overworked goalie. Ryan Harding's header from a free-kick flashed past the post. McGurn nearly gifted an equaliser when, under a challenge from Mark Campbell, he flapped at a Sean Kilgannon free-kick and the ball scraped the post as it went behind.
'Ton went two up seven minutes after the break. Paul McGowan combined with Jamie Stevenson and the latter's shot was deflected past Brown by Campbell's heel.
Templeman curled a shot inches wide after Brown failed to cut out a James McAlister cross and the 'keeper was literally knocked off his feet by a tremendous left-footed drive by Man-of the Match, Templeman.
Paul McManus spurned a wonderful chance to narrow the deficit when sent clear by Stephen Manson but his low drive, although it beat McGurn, struck a post.