Raith Rovers opened up a three-point gap between themselves and First Division bottom club Queen of the South, despite being pegged back at Morton.
Paul Di Giacomo skewed his shot wide as the hosts threatened in the first half.
Team-mate Archie Campbell's well-struck volley was parried by goalkeeper David McGurn after the break.
The visitors took the lead on 55 minutes when Grant Murray bulleted a header home from Joe Hamill's cross.
But Morton were level 10 minutes later as David O'Brien converted Campbell's cross with a measured volley.
McGurn saved another volley, this time from Marc Smyth, 15 minutes from the end.
Stewart, Weatherson, Graham, Smyth, O'Ware, Di Giacomo (McGeouch 60), Bachirou, Tidser, O'Brien, Campbell (Fitzharris 83), MacDonald (Hawke 90). Subs Not Used: McGinley, Little.
McGurn, Donaldson, Murray, Davidson, Dyer, Williamson, Allan Walker, Hamill, Baird (Jamie Walker 85), Clarke, Casalinuovo (Smith 72). Subs Not Used: Laidlaw, Colin Wilson, Ellis.