Alloa won for the first time in eight games, overcoming a spirited Morton performance to win 1-0 at Cappielow Park.
Morton made a good start but were soon behind, as Ryan McCord scored the only goal of the game after 18 minutes, after being found inside the box by a fine Graeme Holmes pass.
Alloa were lucky not to be reduced to 10 men soon after, as Stephen Simmons appeared to kick out at Fouad Bachirou for following through on a tackle.
Dougie Imrie had a great chance to level things up, but he missed an open goal after Alloa keeper Scott Bain headed the ball straight out to the Morton striker.
A combination of poor finishing and good goalkeeping meant that Morton were unable to draw level, before Imrie was sent off late on for bringing down substitute Derek Riordan when through on goal.