Goals from Michael Gardyne and Steven Milne saw Ross County secured maximum points at Morton's expense.
Derek Lyle and Brian Graham both headed over for Ton before Gardyne broke the deadlock when he fired home Jason Marr's cross.
Morton pressed for an equaliser but their hopes were dashed when County extended their lead.
Milne directed Richard Brittain's cross low into the net to seal County's win.
Ross County: McGovern, Marr (Miller 69), Fitzpatrick, Lawson, Boyd, Flynn, Milne, Vigurs (Kettlewell 79), Barrowman, Brittain, Gardyne (Corcoran 88). Subs Not Used: Malin, Wood.
Goals: Gardyne 46, Milne 86.
Morton: Cuthbert, Evans, Monti, Smyth, McCaffrey, Tidser, Holmes (O'Brien 59), Bachirou, Lyle (Kean 72), Graham (Weatherson 63), Jenkins. Subs Not Used: Stewart, McKinlay.
Booked: Graham, McCaffrey, Evans.
Ref: Stevie O'Reilly