Inverness Caley Thistle moved into fourth place to remain on the periphery of the Championship title race.
Morton were positive from the outset and after five minutes Michael Tidser was on target with an effort which Caley goalkeeper Mark Ridgers did well to push away.
But it was Inverness who took the led in 17 minutes when Liam Polworth chested the ball through to Tom Walsh, who drew goalkeeper Derek Gaston and lashed the ball into the net.
The Cappielow side were reduced to ten men in 34 minutes when Kerr Waddell hauled down George Oakley in front of goal, but Sean Welsh failed to convert from the spot.
Caley began the second period determined to atone and in 48 minutes Polworth had a drive tipped over by Gaston. From the corner Tom Walsh curled the ball over for captain Aaron Doran to head the ball in via the underside of the crossbar.
Morton threw themselves a lifeline in 73 minutes when substitute Scott Tiffoney fired low past Ridgers from 20 yards.