Rovers nearly went ahead early on when Neil Jablonski rose to a Brian Fairbairn corner but his header glanced off the bar with Stef Gonet beaten.
Andy McLaren posed several problems down the right for Rovers and Iain Davidson saved the visitors when he headed a cross from the veteran over his own bar.
Both sides changed formations in an attempt to break the deadlock but it was only late in the first half when Morton seriously threatened. Chris Millar's cross was headed on to the bar by Peter Weatherson with Alistair Brown and his defenders in disarray.
Chris Templeman missed a fine chance to give 'Ton the lead just after the break but Rovers came into things more, Paul McManus mistiming a header and Gonet fumbling a stinging shot from the same player.
Fairbairn drove wide but Raith lost Willie Lyle when he was sent off for his second yellow card, both for fouls on the speedy Jim McAlister. Visiting manager, Gordon Dalziel, was sent to the stand as he sought to rearrange his defensive set-up.
Immediately, Chris Millar knocked in a high cross from Alex Walker from eight yards. Substitute Chris McLeod lasted less than a minute, dismissed for a 'last man' foul on Weatherson.
Brown gallantly kept out further Morton scoring attempts before he was beaten three minutes from the end, McLaren's shot from fifteen yards being deflected past him by Tod Lumsden.