Brian Graham's long-range lob went just over the crossbar as the home side started to apply the pressure.
Morton had chances to win the game in the second half, but Peter Weatherson directed his two shots on target.
Morton: Cuthbert, Evans, Smyth, McCaffrey, Monti, Lyle, Jenkins, Bachirou, Tidser, Graham, Kean (Weatherson 70). Subs Not Used: Stewart, O'Brien, Holmes, Kane. Booked: Graham.
Raith: McNeil, Craig Wilson, Campbell, Murray, Hill (Dyer 85), Walker, Davidson, Simmons, McBride, Baird, Tade. Subs Not Used: McGurn, Ferry, Weir, Wales.
Booked: Davidson, Simmons.
Att: 1,809
Ref: Crawford Allan
Source: BBC Sport
Source: BBC Sport